Question

A man is parasailing above a lake at an angle of elevation of 32° from a boat. If 129.5 meters of line connects the boat to the parasail, how many meters above the lake is the man to the nearest tenth of a meter? A) 68.6 m B) 80.9 m C) 109.8 m D) 152.7 m

Answer 1

Answer:

The correct  answer is  option A) 68.6 m

Step-by-step explanation:

Given:

The angle of elevation from the boat  = 32 degrees

Length of the cable that connects the boat and the man = 129.5 meters

To Find:

How many meters above the lake is the man to the nearest tenth of a meter = ?

Solution:

Let the  height of the man from the Lake be H.

then H can be found using the sine formula of the right tringle

where

$sin( angle) = \frac{opposite}{hypotenuse}$

In the figure below

the hypotenuse is the cable length, H is the opposite side

and angle is the angle of elevation:

The substituting the values

$sin(32^{\circ}) = \frac{H}{129.5}$

$H = 129.5 \times sin(32)$

$H = 0.5299 \times 129.5$

H = 68.624

H= 68.6