The following problem requires multiple triangles to solve. As before, draw an appropriate diagram and add any calculated values to the diagram as you go.

 

Example 2

Two buildings are 10 m apart. From the top of the shorter building, the angle of elevation to the top of the taller building is 61°, and the angle of depression to the base of the taller building is 72º. How tall, to the nearest tenth of a metre, is each building?

  Begin by sketching a diagram of the scenario.

Let b represent the height of the grey building and let a + b represent the height of the brown building. Both a and b can be determined using a tangent ratio.

The shorter, grey building is approximately 30.8 m tall and the taller, brown building is approximately 48.8 m tall.