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Example: Trig to solve the sides and angles of a right triangle | Trigonometry | Khan Academy

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Use sine when solving for a side:
sin90= x/5
5sin90=x

Use sine inverse when solving for an angle:
sinx=5/8
sin^-1(5/8)=x

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A triangle with an angle of 90 degrees.

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To solve a right triangle you will need to use the information you are given to find the rest of the triangle. If you are solving for an angle use SOHCATOA. If you are solving for a side use Pythagorean's theorem.

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Sine= Opposite/ Hypotenuse
Cosine= Adjacent/ Hypotenuse
Tangent= Opposite/ Adjacent

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a^2 + b^2 = c^2

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In this problem you are given the angle and side for a. Since you know 2 of the 3 angles, you can add your given angles and subtract from 180. This gives you angle B which is 73 degrees. Knowing one side means we will have to use SOHCAHTOA and Pythagorean's theorem. We will use SOCAHTOA first to solve for side b. We will use tangent. tan= opp./ adj. So tan17= 135/b. Plug that into the calculator and you get b to equal  441.6. Using Pythagorean's theorem we can solve for c, the last side. We do 135^2 + 441.6^2 = c^2. Once you do the math this comes out to be c=461.7.

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In this problem you are given the angle for h and two other sides. We will solve for x first. Since we have the adjacent side and the opposite side for x we will use tangent to solve. tanX=6/8. To do this we will use tangent inverse. We get the angle to be 37 degrees. If we add this to 90 and subtract from 180 we get the third angle to be 53 degrees. Now we can use Pythagorean's theorem to solve for h, the last side. h is the hypotenuse. 6^2 + 8^2= c^2. The last side is 10.