Question

I don’t understand how to find the height

Answer 1

Answer:

height, x is 235 ft

Step-by-step explanation:

From trigonometric ratios:

$\cos( \theta) = \frac{adjacent}{hypotenuse}$

but:

$\theta = 90 \degree - 36 \degree \\ \theta = 54 \degree$

adjacent is x

hypotenuse is 400 ft

$\ \cos ( 54 \degree) = \frac{x}{400} \\ \\ x = 400 \ \cos (54 \degree) \\ x = 235 \: \: feet$

Answer 2

Answer:

$235\ ft$

Step-by-step explanation:

In this problem, one is given two parallel lines and a few transversals that form a triangle between these parallel lines. The parallel lines, one from the parasailer, and one from the boat have an angle of depression between them. This means the angle of elevation from the boat to the parasailer is also (36) degrees. This is due to the alternate interior angles theorem, which states that when two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.

The triangle formed in this situation is a right triangle, this is indicated by the box around one of the angles. Now that one has found another angle measure in this triangle, one can use right angle trigonometry. Right angle trigonometry is a series of ratios that describe the relationship between the sides and angles of a right triangle. These ratios are as follows:

$sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}$

Please note that the names (opposite) and (adjacent) are subjective, and change relative to the angle one is looking at, however (hypotenuse) refers to the side opposite the right angle. This side doesn't change its name. In this situation, it would be most logical to use the ratio of sine, (sin), as one has the measure of the hypotenuse, and one is trying to find the measure of the side opposite the angle. Substitute the given information into the ratio of (sin) and solve to find the unknown:

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

$sin(36)=\frac{x}{400}$

Inverse operations,

$sin(36)=\frac{x}{400}$

$400(sin(36))=x$

$235.114=x$