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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #5 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(18)}{2}=\frac{36}{2}=18$

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Example Question #1491 : Basic Geometry

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(30)}{4}=\frac{60}{4}=15$

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Example Question #1492 : Basic Geometry

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(60)}{40}=\frac{120}{40}=3$

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Example Question #1493 : Basic Geometry

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(22)}{11}=\frac{44}{11}=4$

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Example Question #1494 : Basic Geometry

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

$\frac{1}{8}$

$\frac{1}{2}$

$\frac{1}{4}$

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(4)}{8}=\frac{8}{8}=1$

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Example Question #1495 : Basic Geometry

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(3)}{3}=\frac{6}{3}=2$

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Example Question #1496 : Basic Geometry

Prblem 8 basic geometry

Find the missing length in triangle ABC.

Possible Answers:

$2\ in$

$5\ in$

$5/4\ in$

$3\ in$

$4\ in$

Correct answer:

$4\ in$

Explanation:

To find the missing length, use the Pythagorean Theorem.

a^2+b^2=c^2

Where "a" and "b" are the legs, and "c" is the hypotenuse.

a=3 inches

b=???

c= 5 inches

Plug in the values

3^2+b^2=5^2

9+b^2=25

Now, get the variable by itself.

b^2=16

Take the square root of both sides.

$\sqrt{b^2}=\sqrt{16}$

b=4

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Example Question #1 : How To Find An Angle In A Right Triangle

Find angle C.

Triangle_90_25_c

Possible Answers:

C=53

C=72

C=65

C=70

None of these

Correct answer:

C=65

Explanation:

First, know that all the angles in a triangle add up to 180 degrees.

Each triangle has 3 angles. Thus, we have the sum of three angles as shown:

180=A+B+C

where we have angles A, B, and C. In our right triangle, one angle is 25 degree and we'll call that angle A. The other known angle is 90 degrees and we'll call this angle B. Thus, we have

180=25+90+C

Simplify and solve for C.

180=115+C

C=65

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Example Question #1 : How To Find An Angle In A Right Triangle

Which of the following can be two angle measures of a right triangle?

Possible Answers:

$35^{\circ},55^{\circ}$

$100^{\circ},10^{\circ}$

$38^{\circ},42^{\circ}$

$60^{\circ},40^{\circ}$

$60^{\circ},60^{\circ}$

Correct answer:

$35^{\circ},55^{\circ}$

Explanation:

A right triangle cannot have an obtuse angle; this eliminates the choice of 100 and 10.

The acute angles of a right triangle must total 90 degrees. Three choices can be eliminated by this criterion:

60+40=100

38+42=80

60+60=120

The remaining choice is correct: 35+55=90

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Example Question #2 : How To Find An Angle In A Right Triangle

A right triangle has an angle that is 15 more than twice the other. What is the smaller angle?

Possible Answers:

Correct answer:

Explanation:

The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90.

Let = first angle and 2x + 15 = second angle

So the equation to solve becomes x+ 2x+15 = 90 or 3x=75

Thus, the first angle is and the second angle is .

So the smaller angle is

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #5 : How To Find The Height Of A Right Triangle

Example Question #1491 : Basic Geometry

Example Question #1492 : Basic Geometry

Example Question #1493 : Basic Geometry

Example Question #1494 : Basic Geometry

Example Question #1495 : Basic Geometry

Example Question #1496 : Basic Geometry

Example Question #1 : How To Find An Angle In A Right Triangle

Example Question #1 : How To Find An Angle In A Right Triangle

Example Question #2 : How To Find An Angle In A Right Triangle

All Basic Geometry Resources

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