You are given the function of identity of cos(6x) = 2cos^2(3x)-1. A sine and cosine function is one of the basic functions encountered in Trigonometry. Sine is equal to the opposite side over hypotenuse whereas the cosine function is equal to the adjacent side over the hypotenuse.

4 0

3 years ago

If aa skateboard ramp is 15 meters long and it extends 12 meters from the base of the starting point. How high is the ramp?

guapka [62]

The height of the ramp is 9 meter

Solution:

It is given that a skateboard ramp is 15 meters long and it extends 12 meters from the base of the starting point.

If we look at the sum, closely we understand that the ramp is a right angled triangle.

Which has a base length of 12 metres and a hypotenuse of 15 metres.

We need to find its height.

To do so we can use the Pythagoras theorem

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, we get

$\text {Hypotenuse}^{2}=\text {height}^{2}+\text { base }^{2}$

Since we already know the lengths of the hypotenuse and base we can substitute them in the formula and solve for the height.

Let height of the ramp be denoted by ‘h’

$\begin{array}{l}{15^{2}=12^{2}+h^{2}} \\\\ {225=144+h^{2}} \\\\ {225-144=h^{2}} \\\\ {81=h^{2}} \\\\ {h=\sqrt{81}} \\\\ {h=9}\end{array}$

Therefore, the height of the ramp is 9 meter

3 0

3 years ago