Quiz 4.5.3 and 4.5.4 Version B

1. A ladder leans against a house at an angle of elevation of 45 degrees. If the ladder is 10 feet from the bottom of the house, how high up on the house does the ladder reach?

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B

C

D

E

The ladder reaches a height of 10 feet on the house. This can be determined using trigonometry. Since the angle of elevation is 45 degrees, it forms a right triangle with the ladder as the hypotenuse. The adjacent side of the triangle represents the distance from the bottom of the house to the ladder, which is given as 10 feet. Since the angle is 45 degrees, the adjacent and opposite sides of the triangle are equal. Therefore, the ladder reaches a height of 10 feet on the house.

Explanation

The ladder reaches a height of 10 feet on the house. This can be determined using trigonometry. Since the angle of elevation is 45 degrees, it forms a right triangle with the ladder as the hypotenuse. The adjacent side of the triangle represents the distance from the bottom of the house to the ladder, which is given as 10 feet. Since the angle is 45 degrees, the adjacent and opposite sides of the triangle are equal. Therefore, the ladder reaches a height of 10 feet on the house.

2. Find the missing side.

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B

C

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E

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3. Find the missing side.

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4. Find the missing side.

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5. Find the missing side.

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6. Find the missing side.

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7. Find the missing side.

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8. Find the missing side.

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9. Find the diagonal of a square that has sides of length 8.

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B

C

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E

The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the square has sides of length 8, so the length of each side is 8. Using the Pythagorean theorem, we can calculate the length of the diagonal as the square root of (8^2 + 8^2) = √(64 + 64) = √128 = 8√2. Therefore, the correct answer is C.

Explanation

The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the square has sides of length 8, so the length of each side is 8. Using the Pythagorean theorem, we can calculate the length of the diagonal as the square root of (8^2 + 8^2) = √(64 + 64) = √128 = 8√2. Therefore, the correct answer is C.

10. A ladder leans up against a house at an angle of elevation of 60 degrees. If the ladder is 20 feet long, how high up on the house does the ladder reach? You may round to the nearest tenth of a foot.

A

B

C

D

E

The correct answer is B. To find the height that the ladder reaches on the house, we can use trigonometry. The angle of elevation is given as 60 degrees and the length of the ladder is 20 feet. The height on the house can be found using the sine function, which is opposite/hypotenuse. So, the height on the house is equal to the length of the ladder multiplied by the sine of the angle of elevation. Therefore, the height on the house is 20 feet multiplied by the sine of 60 degrees, which is approximately 17.3 feet.

Explanation

The correct answer is B. To find the height that the ladder reaches on the house, we can use trigonometry. The angle of elevation is given as 60 degrees and the length of the ladder is 20 feet. The height on the house can be found using the sine function, which is opposite/hypotenuse. So, the height on the house is equal to the length of the ladder multiplied by the sine of the angle of elevation. Therefore, the height on the house is 20 feet multiplied by the sine of 60 degrees, which is approximately 17.3 feet.

Quiz 4.5.3 And 4.5.4 Version B