Exercise 43 Page 467

We are told that a person is standing $75$ meters from the base of the Jian Mao Building. We also know that this person's eye level is $1.5$ meters above the ground. The person estimates that the angle of elevation to the top of the building is about $80^{\circ }.$ Let's sketch a diagram to show this situation!

Since we know an acute angle and its adjacent side, we can recall the trigonometric ratio for tangent to find the height $h$ from eye level to the top of the building. In our case the length of the adjacent side is $75,$ the length of the opposite side is $h,$ and the measure of the angle is $80^{\circ }.$ Let's solve this equation for $h$! Now, we will find the height $H$ of the building from the ground by adding the height $h$ to the distance between the ground and the eye. The height is about $427$ meters.