# Problem Solving with Trigonometry (Right-Angle Triangles)

In order to measure the height of a tree, Dan calculated that its shadow is $$12\;[m]$$ long and that the line joining the top of the tree to the tip of the shadow forms an angle of $$52°$$. Find the height of the tree to the nearest metre.

At the top of a hiking trail, there are 2 vertical posts. One is $$5\;[m]$$ tall and the other is $$7\;[m]$$ tall. The ground between the posts is level, and the bases of the posts are 4m apart. The posts are connected by 2 straight wires.
i. What angle does each wire make with the ground?
ii. What is the length of each wire?

Aimee and Russell are facing each other on opposite sides of an $$8\;[m]$$ telephone pole. From Aimee's point of view, the top of the telephone pole is at an angle of elevation of $$52°$$. From Russell's point of view, the top of the telephone pole is at an angle of elevation of $$38°$$. How far apart are Aimee and Russell?

From the top of the building, the angle of elevation of the top of a nearby building is $$28°$$ and the angle of depression of the bottom of a nearby building is $$48°$$. The distance between the 2 buildings is $$50\;[m]$$. What is the height of the taller building?