Geometry - Loudoun County Public Schools



Geometry Name_________________________

DAY 7 WARM UP Date _______________

1. The angle between the bottom of a fence and the top of a tree is 75°.

The tree is 4 feet from the fence. How tall is the tree? Round your answer

to the nearest foot.

x

Find the value of x to the nearest tenth.

2. 3.

Classify each angle as an angle of elevation or an angle of depression.

4. 5.

6. Find the value of each variable.

[pic]

Day 7 Today, we will understand how to solve for all angles and sides in a right triangle.

At the end of today, you will be able to find all side lengths and angles using trigonometric ratios.

Solving Right Triangles

to solve a right triangle –

you must know either:

- two side lengths

- one side length and one acute angle

Inverse Trigonometric Ratios

inverse sine - If sin A = x, then sin-1 x = m[pic]A

inverse cosine - If cos A = y, then cos-1 y = m[pic]A

inverse tangent - If tan A = z, then tan-1 z = m[pic]A

Examples

1. Use a calculator to approximate the measure of [pic]A to the nearest tenth of a degree. Then find [pic]C.

2. Let [pic]A and [pic]B be acute angles in a right triangle. Use a calculator to approximate the measures of [pic]A and [pic]B to the nearest tenth of a degree.

a. sin A = 0.87 b. cos B = 0.15

c. tan A = 0.24 d. sin B = 0.56

3. Solve the right triangle. Round decimals to the nearest tenth.

4. Solve the right triangle. Round decimals to the nearest tenth.

5. Solve the right triangle. Round decimal answers to the nearest tenth.

6. The angle of elevation from a point 25 feet from the base of on a level ground to the top of the tree is 30°. Find the height of the tree.

Worksheet – Practice solving right triangles

Solve the right triangle. Round decimal answers to the nearest tenth.

1. 2.

3. 4.

Let [pic] be an acute angle in a right triangle. Approximate the measure of [pic] to the nearest tenth of a degree.

5. sin A = 0.36 6. tan A = 0.8 7. sin A = 0.27 8. cos A = 0.35

9. A dead tree was struck by lightning, causing it to fall over at a point 10 feet up from its base. If the fallen treetop forms a 40° angle with the ground, how tall was the tree originally to the nearest foot?

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75°

4 ft

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