A 1.6 km road rises 400 m. What is the angle of elevation of the road to the nearest degree?

angle-of-elevation

#1

A 1.6 km road rises 400 m. What is the angle of elevation of the road to the nearest degree?

Answer:

sin(angle of elevation)=400/1600=0.25
angle of elevation=arsin(0.25)]≈14.5

Well the longer side of the triangle is 1600 m and the side opposite of the angle is 400 meters
so if you remember SOH_CAH_TOA we have opposite and the hypotenuse. so we know
sin(theta) = O / H so if we plug in we get sin(theta) = 400 / 1600 and if we solve for theta we get theta = sin-1(400 / 1600). And you can just plug that into your calculator.