Special Triangles – Practice Problems

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Two special right triangles are the 30-60-90 and the 45-45-90 triangles.

For a 30-60-90 triangle, the ratios of the side lengths are 1:√3:2. The smallest side is opposite 30º while the longest side, or hypotenuse, is opposite 90º. In a 45-45-90 triangle, the ratio of the side lengths are 1:1:√2. The longest side, or hypotenuse, is opposite 90º. When solving for the missing length of a side of a special right triangle given the length of one of its sides, use the Pythagorean Theorem and take note of the relevant side ratio to use.

A knowledge of special triangles has several applications in engineering works and construction.

Define trigonometric ratios and solve problems involving right triangles.

CCSS.MATH.CONTENT.HSG.SRT.C.8

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Exercises in this Practice Problem
Solve for the height and distance travelled on land of the plane.
Calculate the distance Grandpa Lindbergh's plane will fall.
Determine the length of the missing side.
Find the distance Grandpa Lindbergh has to fly to get to a height of 1500 feet.
State what a triangle with two 45° angles is called and what is special about it.
Calculate the length of the wooden slats needed to build the kite.