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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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Example Question #15 : How To Find An Angle In A Right Triangle

Find the measurement of .

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to 180 . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

41+90+x=180

131+x=180

x=49

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Example Question #16 : How To Find An Angle In A Right Triangle

Find the measurement of .

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to 180 . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

21+90+x=180

111+x=180

x=69

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Example Question #17 : How To Find An Angle In A Right Triangle

Find the measurement of .

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to 180 . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

26+90+x=180

116+x=180

x=64

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Example Question #21 : How To Find An Angle In A Right Triangle

Find the measurement of .

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to 180 . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

33+90+x=180

123+x=180

x=57

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Example Question #21 : How To Find An Angle In A Right Triangle

Find the measurement of .

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to 180 . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

38+90+x=180

128+x=180

x=52

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Example Question #1523 : Basic Geometry

Find the measurement of .

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to 180 . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

45+90+x=180

135+x=180

x=45

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Example Question #23 : How To Find An Angle In A Right Triangle

A right triangle has equal legs of 6in , and a hypotenuse of 8.5 in . Find the area.

Possible Answers:

28in

18in

12in

20in

51in

Correct answer:

18in

Explanation:

The equation to find the area of a triangle is:

Area = 1/2 (Base) (Height)

In this problem, both the base and the height are 6in. By plugging in the numbers, we get

Area = 1/2 (6) (6)

Area = 1/2 (36)

Area = 18in

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Example Question #1521 : Basic Geometry

A right triangle has another angle that is 47 degrees. What is the third angle?

Possible Answers:

$90^{\circ}$

$47^{\circ}$

$133^{\circ}$

$43^{\circ}$

$45^{\circ}$

Correct answer:

$43^{\circ}$

Explanation:

The inside of a triangle has three angles that total 180 degrees. If one is 47 and the other is the right angle (90).

Then

90 + 47 = 137 .

To find the missing angle subtract the sum above from 180.

180 - 137 = 43 is the degree measurement for the third angle.

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Example Question #541 : Triangles

If one angle of a right triangle measures $70^{\circ}$ , what is the measure of its adjacent angle?

Possible Answers:

$30^{\circ}$

$10^{\circ}$

$80^{\circ}$

$20^{\circ}$

$120^{\circ}$

Correct answer:

$20^{\circ}$

Explanation:

First we need to know that no matter what type of triangle it is, when we add up the measures of all three angles, the total is $180^{\circ}$ . The definition of a right triangle states that one of the three angles measures $90^{\circ}$ . In this problem we know that one of the angles measures $70^{\circ}$ so we add that to $90^{\circ}$ to get a sum of $160^{\circ}$ . To find our missing angle measure we must subtract the sum of the other two angles from the total, giving us an equation that looks like this.

$180^{\circ}-160^{\circ}=20^{\circ}$

So our final answer is $20^{\circ}$

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Example Question #26 : How To Find An Angle In A Right Triangle

Untitled

Refer to the above figure.

True or false: $m \angle C = 30 ^{\circ }$ .

Possible Answers:

False

True

Correct answer:

False

Explanation:

If $m \angle C = 30 ^{\circ }$ , then $\bigtriangleup ABC$ is a 30-60-90 triangle. By the 30-60-90 Triangle Theorem, it would follow that hypotenuse $\overline{AC}$ would be twice as long as shorter leg $\overline{AB}$ - that is,

$\frac{AC}{AB}= 2$ ,

However, since AB = 10 and $AC = 10\sqrt{3}$ , then, substituting,

$\frac{10\sqrt{3}}{10}= \sqrt{3} \ne 2$ .

It follows that $m \angle C\ne 30 ^{\circ }$ .

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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #15 : How To Find An Angle In A Right Triangle

Example Question #16 : How To Find An Angle In A Right Triangle

Example Question #17 : How To Find An Angle In A Right Triangle

Example Question #21 : How To Find An Angle In A Right Triangle

Example Question #21 : How To Find An Angle In A Right Triangle

Example Question #1523 : Basic Geometry

Example Question #23 : How To Find An Angle In A Right Triangle

Example Question #1521 : Basic Geometry

Example Question #541 : Triangles

Example Question #26 : How To Find An Angle In A Right Triangle

All Basic Geometry Resources

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