I have three questions that I need help to answer.
1) a balloon on the end of a string attached to the ground is being blown by the wind. If the ballon us 12.75 m above the ground and the string makes an angle of 48 degrees to the horizontal, what is the length of the string, rounded to two decimal places?
2) A ramp is 9.4 m long and joins two levels, one 3.1 m higher than the other. What angle does the ramp make with the lower level, rounded to one decimal place?
3) A lifeguard on watch at a beach spots a shark at an angle of depression of 9 degrees. If the lifeguard views the shark from a height (to his eye-level) of 16 m above sea-level, what is the horizontal distance between the life guard and the shark to the nearest meter?
Looks like time to review the basic trig functions. It always helps to draw a diagram.
(1) 12.75/x = sin 48°
(2) sin x = 3.1/9.4
(3) 16/x = tan 9°
Sure, I can help you with these questions. Let's break down each question and explain how to find the answers.
1) To find the length of the string, we can use trigonometry. The string, balloon, and ground form a right triangle. The given information tells us that the balloon is 12.75 m above the ground and the string makes an angle of 48 degrees with the horizontal.
Using the trigonometric ratio called sine, we can set up the following equation:
sin(48°) = opposite / hypotenuse
We want to find the hypotenuse, which is the length of the string. Rearranging the equation, we get:
hypotenuse = opposite / sin(48°)
Plugging in the values, we have:
hypotenuse = 12.75 m / sin(48°)
Using a calculator and rounding to two decimal places, we can find the length of the string.
2) In this question, we need to find the angle that the ramp makes with the lower level. Again, we can use trigonometry.
The given information tells us that the ramp is 9.4 m long, and it joins two levels that are 3.1 m apart vertically.
We can set up the following equation using the trigonometric ratio called tangent:
tan(angle) = opposite / adjacent
In this case, the opposite side is the height difference of 3.1 m, and the adjacent side is the length of the ramp, 9.4 m.
tan(angle) = 3.1 m / 9.4 m
Now, we can solve for the angle by taking the inverse tangent (arctan) of both sides:
angle = arctan(3.1 m / 9.4 m)
Using a calculator and rounding to one decimal place, we can find the angle.
3) Lastly, for the third question, we need to find the horizontal distance between the lifeguard and the shark.
Given that the angle of depression (angle below the horizontal) is 9 degrees and the height of the lifeguard's eye-level is 16 m, we can use trigonometry again.
Using the trigonometric ratio called tangent, we can set up the following equation:
tan(9°) = opposite / adjacent
In this case, the opposite side is the height difference of 16 m, and we want to find the adjacent side, which is the horizontal distance.
tan(9°) = 16 m / adjacent
By rearranging the equation, we get:
adjacent = 16 m / tan(9°)
Using a calculator and rounding to the nearest meter, we can find the horizontal distance between the lifeguard and the shark.
I hope this helps you understand how to approach and solve these problems!