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When you have a missing angle in a right triangle, a great way to solve it is to use trigonometry. Trigonometry is the study of a triangles measurements.

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This is the side across from the angle. The angle should not be touching this side. It is used in sine and tangent.

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This is the side that is not the hypotenuse that is touching the point. It is used in cosine and tangent.

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This is the side that is across from the 90 degree angle. It is used in cosine and sine.

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SOH-CAH-TOA is an easy way to remember what to do in a trigonometry problem.

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SOH is used when you have both the opposite and hypotenuse and are looking for the angle. SOH stands for sine-opposite-hypotenuse.

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CAH is used when you have both the adjacent and hypotenuse and are looking for the angle. CAH stands for cosine-adjacent-hypotenuse.

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TOA is used when you have both the opposite and adjacent and are looking for the angle. TOA stands for tangent-opposite-adjacent.

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The angle of elevation is formed by the observers line of sight and a horizontal line. The angle of elevation is always inside the triangle. It is also always the upward angle from the horizontal line.

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When looking down on an object this is formed by a person's line of sight and a horizontal line. The angle of depression is always outside the triangle. When solving an angle of depression problem you can take the angle of depression and apply your corresponding angles rule.

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Tommy the soldier is in the lookout 45 feet off of the ground. He is looking for his friend John the soldier. Tommy is looking out of his lookout with a angle of depression of 40 degrees how far away is John from the base of the lookout.

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To solve this problem you would first take the angle of depression which is 40 degrees and apply your corresponding angle rules. It would move to the bottom right corner. You would then see that you are missing your adjacent side, but you have your opposite side. You should know this is a tangent problem from SOH-CAH-TOA. To set it up it would be tan40=45/x. Switch the x and tan40 places and plug it into the calculator (in degree mode) and wella! You should have gotten 53.6 ft as your answer.

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Nancy the pilot is 300 feet in the air! Nancy took off and has been flying, she has covered the distance of 400 feet. What angle has Nancy been flying at over those 400 feet?