Trigonometry Practice Problems! Math Trivia Quiz

Explanation
The photographer is standing 70 meters away from the building and the angle of elevation is 50 degrees. To find the height of the building, we can use trigonometry. The tangent of the angle of elevation is equal to the opposite side (height of the building) divided by the adjacent side (distance from the building). So, tan(50) = height/70. Rearranging the equation, we get height = 70 * tan(50) = 83.4 meters. Therefore, the height of the building is 83.4 meters.

Explanation
The man is standing at the base of the tower, and he notices that the angle between the ground and the top of the tower is 60 degrees. This forms a right triangle, with the height of the tower as one of the sides and the distance between the man and the tower as the other side. Since we know the height of the tower is 15 meters, and the angle is 60 degrees, we can use trigonometry to find the distance between the man and the tower. By using the sine function (sin(angle) = opposite/hypotenuse), we can calculate the distance to be approximately 8.67 meters.

Explanation
The angle of elevation to the bird can be found using trigonometry. In this case, the opposite side is the height of the tree (200 ft) and the adjacent side is the distance from the man to the tree (75 ft). The angle of elevation can be found using the tangent function: tan(angle) = opposite/adjacent. Therefore, tan(angle) = 200/75. Taking the inverse tangent of both sides, we find that the angle is approximately 69.5°.

Explanation
The angle of depression is the angle formed between the horizontal line and the line of sight from the observer to the object below. In this case, the boat is below the lighthouse. To find the distance of the boat from the lighthouse, we can use trigonometry. We can use the tangent function, which is opposite over adjacent, to find the distance. The opposite side is the height of the lighthouse (100 meters) and the adjacent side is the distance we want to find. By taking the tangent of the angle of depression (6a), we can solve for the distance. Using this method, we find that the distance is approximately 951.4 meters.

Explanation
To find the angle of elevation, we can use the trigonometric function tangent. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the wall (13 feet) and the adjacent side is the length of the ladder (14 feet). Therefore, the tangent of the angle of elevation is 13/14. Using a calculator, we can find that the angle of elevation is approximately 68.4 degrees.

Explanation
The measure of angle θ can be found using the tangent function. Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side is h and the adjacent side is d. Therefore, tan(θ) = h/d. Plugging in the given values, tan(θ) = 15/30 = 0.5. To find θ, we can take the inverse tangent (arctan) of 0.5. Using a calculator, we find that θ ≈ 25.67°.

Explanation
The approximate measure of the angle the ladder forms with the ground can be determined using trigonometry. In this case, we can use the tangent function, which is defined as the ratio of the length of the opposite side (height of the wall) to the length of the adjacent side (distance from the foot of the ladder to the base of the wall). By taking the arctangent of this ratio, we can find the angle. Using the given values, the tangent of the angle is approximately 0.364, and taking the arctangent of this value gives us an approximate angle of 69.5°.

Explanation
The answer is 5 because in a right triangle, the side opposite to a 45-degree angle is equal to the side adjacent to the angle. Since the opposite side is given as 5, the adjacent side (which is also the value of x) would also be 5.

Explanation
The sine of angle A can be found by dividing the length of the side opposite angle A by the length of the hypotenuse in a right triangle. In this case, the side opposite angle A is 4 and the hypotenuse is 5. Therefore, the sine of angle A is 4/5.

Explanation
To determine the length of the ramp, we can use trigonometry. Since the ramp needs to be pitched at 30 degrees, we can use the sine function to find the length. The formula to find the length of the ramp is: length = height / sin(angle). Plugging in the values, we get: length = 25 / sin(30). Using a calculator, we find that sin(30) is 0.5. So, length = 25 / 0.5 = 50 inches. Therefore, the correct answer is 50 inches.