Geometry

Solving Triangles

Bearing Problems

         

The mast in the above diagram is 99 meters high and a wire is stretched tight to form a straight line to the top of the mast at an angle of 60.60^\circ. How long is the wire in meters?

The length of AC\overline{AC} is 4 and the length of BC\overline{BC} is 222\sqrt{2}. What is the length of AB\overline{AB}?

In the above diagram, the length of the shadow of the building is a=32a=32 meters and the end of the shadow forms an angle of 6060^\circ with the sun. What is the height of the building?

A perfectly straight tree is struck by lightning and breaks at point AA. After falling, the tree forms a triangle with the ground at angle ACB=30\angle ACB =30^\circ and the distance between the top and bottom of the tree is d=27 m, d =27\text{ m}, as illustrated in the above diagram. What is the height of the tree before being struck by lightning?

The mast in the above diagram is 2121 meters high and a wire is stretched tight to form a straight line to the top of the mast at an angle of 60.60^\circ. How long is the wire in meters?

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