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MAT 151: College Algebra with Trigonometry

Subsection 2.2 Right Triangle Trigonometry Exercises

  1. A 12-foot ladder is going to be leaned against a wall. The ladder makes an angle with the ground of \(1.1\) radians. How high up the wall will the ladder make contact with the wall?
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  2. For each triangle below, find all missing sides and angles.
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    1. A right triangle labeled ABC with the right angle at vertex C. The hypotenuse AB is labeled 10 feet, and angle B is labeled 25 degrees.
      Figure 2.2.19.
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    2. A right triangle labeled ABC with the right angle at vertex C. Vertex C is on the right, with a vertical segment from C up to A labeled 3 feet. The hypotenuse connects A to B on the left. Angle B is marked along the horizontal base and labeled pi over nine.
      Figure 2.2.20.
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  3. Find the missing sides and angle.
    A triangle labeled ABC with vertex A at the top, B on the left, and C on the right. The base BC is horizontal. Angle B is labeled 40 degrees, angle C is labeled 55 degrees, and the side from B to A is labeled 5 centimeters.
    Figure 2.2.21.
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  4. Salvador wants to visit four of his favorite fishing spots (A, B, C and D on the diagram below). From shore, he measures the angle to each spot as shown below. He knows that distance from his position on the shore to the fishing spot at point A is 7 miles. How far will he travel, from the starting point on the shore, visiting all four spots, and returning to the shore.
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    A triangle with four 5 points labeled. The top point is labeled shore. On the side opposite the shore are labeled points A, B, C and D from left to right. Angle B is labeled as a right angle. There are lines connecting the point labeled shore to each of the other points. The top angles are labeled pi/4, pi/3 and pi/8 from left to right.
    Figure 2.2.22.
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  5. Perform the indicated operation and simplify if possible.
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    1. \(\displaystyle \frac{y^2-9}{y^2+6y+9}\)
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    2. \(\displaystyle \frac{z^2+2z-3}{3z^2-z-2} \div (z+3)\)
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    3. \(\displaystyle \frac{3-4m}{m^2+3m-10}-\frac{2}{m+5}\)
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