Marnie planted a tree and attached a guy wire to help support its growth. If the guy wire is 4.8 m long and is attached at an angle of elevation of 34o, how high up the tree will it reach?(Round your answer to 1 decimal place, and put only the number in the box with no units.)
Question
Marnie planted a tree and attached a guy wire to help support its growth. If the guy wire is 4.8 m long and is attached at an angle of elevation of 34o, how high up the tree will it reach?(Round your answer to 1 decimal place, and put only the number in the box with no units.)
Solution
To solve this problem, we can use the sine function in trigonometry. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse.
In this case, the guy wire is the hypotenuse of the triangle, the height of the tree is the opposite side, and the angle of elevation is given. We can set up the equation as follows:
sin(34) = height / 4.8
To solve for the height, we multiply both sides by 4.8:
height = 4.8 * sin(34)
Now, we just need to calculate the value.
Using a calculator, sin(34) is approximately 0.5592.
So, height = 4.8 * 0.5592 = 2.68416
Rounding to one decimal place, the height is approximately 2.7.
Similar Questions
The angle of elevation to a nearby tree from a point on the ground is measured to be 32degrees ∘ . How tall is the tree if the point on the ground is 71 feet from the bottom of the tree? Round your answer to the nearest tenth of a foot if necessary.
On the top of the tower 100 meters high, Brianne saw and fell in love with Jo who is sitting under the tree. How far is Jo from the tower if the angle of depression formed by Brianne’s line of sight with the horizontal is 30°?
Ford wants to calculate the height of a Christmas tree so he measures a distance of 9 m from the base of the tree (AC).Next he measures the angle x and finds it to be 160How tall is the tree (BC), rounded to the nearest 2 decimal places.(Put the numbers only in the box, do not enter any units.)
Rachel is a surveyor and looks through her theodolite which is 1.5 m high, and sites the top of a tree from 16.2 m away. Rachel determines that the tree is 8.1 m tall. What is the angle of depression from the top of the tree to Rachel's theodolite?(Round your answer to one decimal and put only numbers with no units in the box.)
A tree is broken by the wind. The top struck the ground at an angle of 30c and at distance of 10 m from its root.The whole height of the tree is ( . )3 1 732=(a) m10 3 (b) m3 10(c) m20 3 (d) m
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.