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Basic Geometry : Triangles

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Example Questions

Example Question #21 : 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

20in

12in

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:

$133^{\circ}$

$43^{\circ}$

$47^{\circ}$

$45^{\circ}$

$90^{\circ}$

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

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

Possible Answers:

$80^{\circ}$

$10^{\circ}$

$120^{\circ}$

$20^{\circ}$

$30^{\circ}$

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 #27 : 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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Example Question #22 : How To Find An Angle In A Right Triangle

If one angle of a right triangle is $63^{\circ}$ what is the measure of the third angle?

Possible Answers:

$7^{\circ}$

$37^{\circ}$

$117^{\circ}$

$17^{\circ}$

$27^{\circ}$

Correct answer:

$27^{\circ}$

Explanation:

First we need to know that when we add up all 3 angles of a triangle, the sum will always equal $180^{\circ}$ (this is the case for all types of triangles). Since we know this is a right triangle, first we subtract $90^{\circ}$ (by definition all right triangles equal $90^{\circ}$ ).

$180^{\circ}-90^{\circ}= 90^{\circ}$

We know another angle equals $63^{\circ}$ so we subtract it from $90^{\circ}$ and we get $27^{\circ}$ .

Our final answer is $27^{\circ}$ .

To check our answer we can add up the three angles to make sure we come up with a sum of $180^{\circ}$ .

$90^{\circ}+63^{\circ}+27^{\circ}=180^{\circ}$

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Example Question #1522 : Basic Geometry

Untitled

True or false: $m \angle A = 60 ^{\circ }$

Possible Answers:

False

True

Correct answer:

True

Explanation:

By the 30-60-90 Triangle Theorem, the ratio of the length of the longer leg of a 30-60-90 triangle to that of the shorter leg is $\sqrt{3}$ . In the given triangle, we see that this ratio is

$\frac{BC}{BA} = \frac{10 \sqrt{3}}{10} = \sqrt{3}$ ,

the correct ratio. This is indeed a 30-60-90 triangle, and, $\angle A$ being opposite the longer leg, has measure $60 ^{\circ }$ .

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Example Question #1523 : Basic Geometry

A right triangle has side lengths of 5, 10, and 11.18 inches. One angle is 63.4 degrees. What is the measure of the other angle?

Possible Answers:

$\theta=66.6\hspace{1mm}degrees$

$\theta=26.6\hspace{1mm}degrees$

$\theta=56.6\hspace{1mm}degrees$

None of these.

$\theta=36.6\hspace{1mm}degrees$

Correct answer:

$\theta=26.6\hspace{1mm}degrees$

Explanation:

Since this is a right triangle, simply add this right angle to the given angle and subtract from 180 degrees.

The side lengths are not relevant in this problem.

$180-(90+63.4)=\mathbf{26.6}$

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

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

Example Question #1521 : Basic Geometry

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

Example Question #27 : How To Find An Angle In A Right Triangle

Example Question #22 : How To Find An Angle In A Right Triangle

Example Question #1522 : Basic Geometry

Example Question #1523 : Basic Geometry

All Basic Geometry Resources

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