Question

Building a and b are across the street from each other,35 metres apart. From a point on the roof of building a the angle of elevation at the top of building b is 24°, and the angle of depression of the base of building b is 34°. How tall is each building ​

Answer 1

Let's let h be the height of building B, and let x be the distance between the point on the roof of building A and the base of building B. We can use the tangent function to set up two equations with two unknowns:

tan(24) = h / x

tan(34) = h / (x + 35)

We can solve for h by eliminating x from these equations. We can do this by solving the first equation for x and substituting into the second equation:

x = h / tan(24)

tan(34) = h / (h / tan(24) + 35)

Simplifying this equation, we get:

h = (35 * tan(24) * tan(34)) / (tan(34) - tan(24))

Plugging in the values, we get:

h = 22.7 meters

So building B is 22.7 meters tall. To find the height of building A, we can use the equation:

x = h / tan(24)

Plugging in the values, we get:

x = 55.1 meters

So building A is 55.1 meters tall.