Question

The coordinates of the point Q are (2, h) and ∠POQ= 60°.

Answer 1

Answer:

Step-by-step explanation:

Use right triangle trig here...the 30-60-90 right triangle to be specific. We have the 60 degree angle as the reference angle. That means that the 90 degree angle is the other base angle and the 30 degree angle is the vertex angle (the angle at the top). In a 30-60-90 Pythagorean Triple, the side across from the 30 degree angle measures x, the side across from the 60 degree angle measures x√3, and the side across from the 90 degree angle (this side is also called the hypotenuse!) measures 2x. If we can find the measure of x, then we will multiply it by 2 to get the length of OQ, the hypotenuse.

The side across from the vertex angle is the distance along the x-axis, which we know to be 2. That means that x = 2. Therefore, the length of the hypotenuse, 2x, is 2(2) which is 4.

h is the same as the length of the side across from the 60 degree angle. The side across from the 60 degree angle is x√3. We already know that x = 2, therefore, h = 2√3.