Find the height of the tower to the nearest tenth of a meter. the dimensions are 58 degrees and 36m. [its a right angle triangle]
Why did the tower bring a ladder to the math competition? Because it wanted to "climb" to the top of the class! Now, let's tackle this problem together.
In a right triangle, we can use trigonometry to find the missing side lengths. Since we know the angle and the length of one side, we can use the tangent function.
Let's call the height of the tower "h." We can set up the equation:
tan(58°) = h/36
Now, we can solve for h:
h = tan(58°) * 36
Calculating this, we find that the height of the tower is approximately 55.3 meters (rounded to the nearest tenth). So, the height of the tower is 55.3 meters in length.
To find the height of the tower, we can use trigonometry. In a right-angled triangle, the tangent of an angle is equal to the ratio of the length opposite the angle to the length adjacent to the angle.
In this case, we know the angle is 58 degrees (let's call it angle A) and the adjacent side is 36 meters (let's call it side B).
The tangent of angle A can be found using the formula tan(A) = opposite/adjacent.
So, tan(58 degrees) = opposite/36.
To solve for the opposite, we can rearrange the equation:
opposite = tan(58 degrees) * 36.
Using a calculator, we can find the tangent of 58 degrees:
tan(58 degrees) ≈ 1.6198.
Therefore, the height of the tower is approximately:
opposite ≈ 1.6198 * 36 ≈ 58.3148 meters.
Rounding to the nearest tenth of a meter, the height of the tower is approximately 58.3 meters.