A princess is standing 38 feet from the base of a 217 foot tall tower. What is the angle of elevation from him to the ogre who has his princess held captive

Angle of elevation = 80°

Step-by-step explanation:

A princess is standing 38 feet from the base of a 217 foot tall tower. What is the angle of elevation from him to the ogre who has his princess held captive?

To solve for angle of elevation, we use the Trigonometric function of Tangent.

tan θ = Opposite side/Adjacent side

Opposite side = Height of the tower = 217 ft

Adjacent side = 38ft

tan θ = 217/38

tan θ = 5.6315789474

θ = arc tan 5.6315789474

= 79.930937301°

Approximately = 80°

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus