Solving Right Triangles Word Problems

Remember that the two acute angles will give you different trigonometric function values.Use the Pythagorean Theorem to find the opposite side length. The correct answer is Some problems may provide you with the values of two trigonometric ratios for one angle and ask you to find the value of other ratios.Finding an angle will usually involve using an inverse trigonometric function.

Solving the equation and rounding to the nearest tenth gives you Sometimes you may be given enough information about a right triangle to solve the triangle, but that information may not include the measures of the acute angles.

In this situation, you will need to use the inverse trigonometric function keys on your calculator to solve the triangle.

Note that the hypotenuse is twice as long as the shortest leg which is opposite the 30° angle, so that .

The length of the longest leg which is opposite the 60Since we know all the measures of the angles, we now need to find the lengths of the missing sides.

As a general rule, you need to use a calculator to find the values of the trigonometric functions for any particular angle measure.

However, angles that measure 30°, 45°, and 60°—which you will see in many problems and applications—are special.

If you split the equilateral triangle down the middle, you produce two triangles with 30°, 60° and 90° angles. They both have a hypotenuse of length 2 and a base of length 1.

You can use this triangle (which is sometimes called a 30° - 60° - 90° triangle) to find all of the trigonometric functions for 30° and 60°.

You can find the exact values of these functions without a calculator. Suppose you had a right triangle with an acute angle that measured 45°.

Since the acute angles are complementary, the other one must also measure 45°.

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