Question

Stavros is looking up at a tree that is 42 feet away from him, at an angle of elevation of 23°
23
°
. What is the tree’s height, x, and the distance between Stavros and the top of the tree, y? (1 point)
Responses

x=17.83 ft.
𝑥
=
17.83
ft.
and y=45.63 ft.
𝑦
=
45.63
ft.
x equals 17.83 ft. and y equals 45.63 ft.

x=45.63 ft.
𝑥
=
45.63
ft.
and y=17.83 ft.
𝑦
=
17.83
ft.
x equals 45.63 ft. and y equals 17.83 ft.

x=98.95 ft.
𝑥
=
98.95
ft.
and y=107.49 ft.
𝑦
=
107.49
ft.
x equals 98.95 ft. and y equals 107.49 ft.

x=17.83 ft.
𝑥
=
17.83
ft.
and y=38.03 ft.

Answer 1

Use trig. Let horizontal distance = 42 ft, angle = 23°.

x = 42·tan(23°) ≈ 42·0.4245 = 17.83 ft.
y = 42 / cos(23°) ≈ 42 / 0.9205 = 45.63 ft.

So x ≈ 17.83 ft and y ≈ 45.63 ft (the first choice).