# SAT II Math I : Right Triangles and Similar Triangles

## Example Questions

### Example Question #1 : Right Triangles And Similar Triangles Find the area of the triangle.      Explanation: Dropping the altitude creates two special right triangles as shown in the diagram.  Use the area formula of a triangle to get ### Example Question #1 : Right Triangles And Similar Triangles

Fire tower A is miles due west of fire tower B.  Fire tower A sees a fire in the direction degrees west of north.  Fire tower B sees the same fire in the direction degrees east of north.  Which tower is closer to the fire and by how much?

Fire tower A; 0.24 miles

The two fire towers are equidistant to the fire.

Fire tower A; 1.53 miles

Fire tower B; 0.24 miles

Fire tower B; 1.29 miles

Fire tower B; 0.24 miles

Explanation: First, realize that the angles given are from due north, which means you need to find the complements to find the interior angles of the triangle.  This triangle happens to be a right triangle, so the fast way to compute the distances is using trigonometry.    Fire tower B is miles closer to the fire.

### Example Question #1 : Right Triangles And Similar Triangles Find the length of side .      Explanation:

In an angle-side-angle problem, Law of Sines will solve the triangle.

First find angle A: Then use Law of Sines. ### Example Question #1 : Right Triangles And Similar Triangles

What is the length of the leg of a right triangle whose hypotenuse is 5cm and other leg is 4cm?      Explanation: One leg is 4cm and the hypotenuse is 5cm. Plug in 4 for one of the legs and 5 for the hypotenuse (c).  Subtracting 16 from either side of the equation gives us: The last step is to take the square root both sides resulting in: ### All SAT II Math I Resources 