Using Right Triangles in the Real World EQ: How do you use right triangles in the real world? M2 Unit 2: Day 5

Find the height h of the lamppost to the nearest inch. EXAMPLE 3 Using tangent Remember…SOHCAHTOA Example 1 Find the height h of the lamppost to the nearest inch. tan 70o = opp. adj. Write ratio for tangent of 70o. tan 70o h. = 40. Substitute. Multiply each side by 40. 40 ● tan 70o = h 109.9 h Use a calculator to simplify. ANSWER The lamppost is about 110 inches tall. 2

EXAMPLE 4 Example 2 Find a hypotenuse using an angle of depression You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21o. About how far do you ski down the mountain? About 3349 feet 3

Example 3: loading dock 4 ft ramp 32°

Example 4: You lean a 16 foot ladder against the wall. If the ladder forms a 35° with the ground, how far up the wall does the ladder reach? 16ft 35°

Example 5:

Example 6 Hints: What’s the difference in the heights of the 2 buildings? You must find the measure of the angle adjacent to the angle of depression. 35o 120 x

Example 7:

Example 8 Use a trigonometric ratio to find a hypotenuse EXAMPLE 3 You want to string cable to make a dog run from two corners of a building, as shown in the diagram. Write and solve a proportion using a trigonometric ratio to approximate the length of cable you will need. sin 35o = opp hyp x = 11. sin 35o sin 35o = 11 x x ≈ 11. 0.5736 x ●sin 35o = 11 x ≈ 19.2 ANSWER You will need a little more than 19 feet of cable. 9

Homework: Handout