ACT 1 Geo: Recognize right triangles

$Q_{1}:$ In a construction project, you need to find the height of a tall building. Which trigonometric ratio would you use to solve this problem?

$Q_{2}:$ You're trying to determine the angle of elevation to the top of a mountain. What trigonometric ratio would be most useful in this situation?

$Q_{3}:$ In a right triangle, the side opposite the right angle is called:

$Q_{4}:$ If you know the length of the hypotenuse and one of the acute angles in a right triangle, which trigonometric ratio can you use to find the length of the opposite side?

$Q_{5}:$ A ladder is leaning against a wall. To find how far up the wall the ladder reaches, you can use which trigonometric ratio?

$Q_{6}:$ If you're given the lengths of the two shorter sides of a right triangle, what trigonometric ratio can you use to find one of the acute angles?

$Q_{7}:$ A flagpole casts a shadow of $12$ meters when the sun is at a $30$-degree angle. What is the height of the flagpole?

$Q_{8}:$ You're flying a kite, and the angle of elevation to the kite is $60$ degrees. If the string is $100$ meters long, how high is the kite above the ground?

$Q_{9}:$ If the length of the hypotenuse in a right triangle is $10$ units and one acute angle is $30$ degrees, what is the length of the side opposite that angle?

$Q_{10}:$ A ladder is placed against a wall at a $45$-degree angle. If the ladder is $8$ meters long, how high on the wall does it reach?

$Q_{11}:$ You are on a boat in the middle of a river. You need to determine the width of the river. You measure the angle of your line of sight to a tree on the opposite bank, and it is $30$ degrees. If you know you are $100$ meters downstream from directly across the river, what is the width of the river?

$Q_{12}:$ A person is flying a kite on a windy day. The angle of elevation to the kite is $60$ degrees, and the kite string is $50$ meters long. How high is the kite above the ground?

$Q_{13}:$ You are a surveyor working on a construction site. You need to find the height of a vertical tower, but you cannot directly measure it. You stand $40$ meters away from the base of the tower and measure the angle of elevation to the top as $45$ degrees. What is the height of the tower?

$Q_{14}:$ You're standing at the base of a hill, and the angle of elevation to the top of the hill is $20$ degrees. If you walk $500$ meters towards the hill and then measure the angle of elevation again, what should you expect the new angle to be?

$Q_{15}:$ In a right triangle, if the length of the hypotenuse is $5$ units and the length of one leg is $3$ units, what is the length of the other leg?

$Q_{16}:$ A tree casts a shadow of $8$ meters when the angle of elevation to the sun is $60$ degrees. What is the height of the tree?

$Q_{17}:$ If the angle of elevation to the top of a building is $45$ degrees and you're $20$ meters away from the base of the building, how tall is the building?

$Q_{18}:$ In a right triangle, if the length of one leg is $6$ units and the length of the other leg is $8$ units, what is the length of the hypotenuse?

$Q_{19}:$ You're on a ship, and the angle of depression to a buoy in the water is $15$ degrees. If you're $40$ meters above sea level, how deep is the water at the location of the buoy?

$Q_{20}:$ If the length of the hypotenuse in a right triangle is $13$ units, and one leg is $5$ units long, what is the length of the other leg?

$Q_{21}:$ You're at the top of a building, and the angle of depression to a car on the street below is $30$ degrees. If the building is $50$ meters tall, how far is the car from the base of the building?

$Q_{22}:$ If the angle of elevation to the top of a mountain is $75$ degrees and you're $800$ meters away from the base of the mountain, how tall is the mountain?

$Q_{23}:$ In a right triangle, if the length of the hypotenuse is $17$ units, and one leg is $8$ units long, what is the length of the other leg?

$Q_{24}:$ You're flying a kite, and the string makes an angle of $40$ degrees with the ground. If the string is $80$ meters long, how high is the kite above the ground?

$Q_{25}:$ If the angle of elevation to the top of a building is $60$ degrees and you're $100$ meters away from the base of the building, how tall is the building?