Real-World Applications

EQ: How do you solve a right triangle?

M2 Unit 2: Day 7

Example 1:You are hiking up a mountain peak. You begin hiking at a trailhead whose elevation is about 9400 ft. The trail ends near the summit at 14,255 ft. The horizontal distance between these two points is about 17,625 ft. Estimate the angle of elevation from the trailhead to the summit.

opposite side: 14,255ft-9,400ft 4,85= 5 ft

4855tan

17625A

1 4855tan ( )

17625 15.4

Example 2:

a.

b.

17sin

240A 1 17

sin ( )240

4.1 Convert20 ft to in

To minimize horizontal distance use the greatest possible ramp angle

8tan(4.76 )

x

96.1 in.x

Example 3: MONSTER TRUCKS A monster truck drives off a

ramp in order to jump onto a row of cars. The ramp has a height of 14 feet and a horizontal length of 26 feet. What is the angle θ of the ramp? Round your answer to the nearest integer, if necessary.

14 ft

26 ft

14tan

26 1 14

tan ( )26

28.3

EXAMPLE 5Find leg lengths using an angle of elevation

SKATEBOARD RAMP

You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp.

sin 26o=

opp. hyp.

sin 26o x =14

14 sin 26o = x 6.1 x

Find the height.

The height is about 6.1 feet.

cos 26o=

adj. hyp.

Find the length of the base.

cos 26o y =14

14 cos 26o

= y

12.6 y

The length of the base is about 12.6 feet.

Example 4

Using Pythagorean Theorem

Find the length of the missing side

12

11

Using Pythagorean Theorem

Find sin

10

5

q

q

Using Pythagorean Theorem

Find cos

11

15

q

q

Begin working on your Unit 2 Review