Question

A right triangle contains a 50° angle. (a) If one leg has length 8 inches, what is the length of the hypotenuse? (b) There are two answers. How is this possible? (a) What is the length of the hypotenuse if one leg has length 8 inches? (Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed. Use a comma to separate answers.) (b) How is it possible for there to be more than one answer? O A. Triangles have three sides and only one side is given. B. The given side could be adjacent or opposite the given angle. C. The angle could be in degrees or radians. D. There is only one answer. A building that is 540 feet tall casts a shadow 90 feet long. What is the angle of elevation of the Sun? The angle of elevation is degrees. (Round to the nearest tenth as needed.) B Consult the figure. To find the length of the span of a proposed ski lift from A to B, a surveyor measures the angle DAB to be 25 and then walks off a distance of L = 1650 feet to C and measures the angle ACB to be 15. What is the distance from A to B? D A 1 The distance from A to B is approximately feet. (Do not round until the final answer. Then round to two decimal places as needed.) Barbados A cruise ship maintains a speed of 16 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of 14 off a direct heading to Barbados. The captain maintains the 16-knot speed for 14 hours, after which time the path to Barbados becomes clear of storms. (a) Through what angle should the captain turn to head directly to Barbados? (b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 16-knot speed is maintained? 14" San Juan (a) The captain should head through an angle of ° (Do not round until the final answer. Then round to one decimal place as needed.) (b) The time it will take for the ship to reach Barbados is nours. (Do not round until the final answer. Then round to one decimal place as needed.)

Answer 1

(a) To find the length of the hypotenuse in a right triangle with a 50° angle and one leg measuring 8 inches, we can use the trigonometric function sine.

Using the sine function: sin(50°) = opposite/hypotenuse

We know the opposite side is 8 inches, so we can set up the equation: sin(50°) = 8/hypotenuse

To find the length of the hypotenuse, we can rearrange the equation: hypotenuse = 8/sin(50°)

Using a calculator, we can calculate sin(50°) to be approximately 0.766.

Substituting this value into the equation, we get: hypotenuse = 8/0.766 ≈ 10.43 inches

So, the length of the hypotenuse is approximately 10.43 inches.

(b) There are two possible answers because the given leg could be adjacent or opposite the given angle. In this case, since we are given the length of the leg and not the angle itself, we cannot determine the exact placement of the leg in relation to the angle. Therefore, there can be two possible triangles with different configurations, resulting in different lengths for the hypotenuse.

Explanation: