The way to do this is to set up a 30 degree angle in a coordinate plane in the first quadrant. I say the first quadrant since the first quadrant goes from 0 to 90 degrees and 30 falls right in that interval. Using the positive x-axis as the initial ray of the 30 degree angle and the terminal ray of the angle as the hypotenuse of a right triangle, if we drop a height from the end of the terminal ray to the x-axis we have formed said right triangle. The angle at the origin is the 30 degree angle. According to the Pythagorean triple for a 30-60-90 triangle, the side across from the 30 degree angle measures 1, which is the height of our triangle. The side across from the 60 degree angle is square root of 3, which is the base of our triangle, and the hypotenuse is 2. The cos identity is the ratio that utilizes the side adjacent to the reference angle over the hypotenuse, which for us is

. That's the third choice down. Finding an "exact" value means that they want you to NOT express your answer in decimal form.
Answer:

Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
Let
x----> the height of cone B
using proportion

<h3><u>S</u><u> </u><u>O</u><u> </u><u>L</u><u> </u><u>U</u><u> </u><u>T</u><u> </u><u>I</u><u> </u><u>O</u><u> </u><u>N</u><u> </u><u>:</u></h3>
According to the question,
- Diameter of circle = 16 in
We are asked to calculate it’s circumference in terms of π.
★ Circumference of circle = 2πr
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Let us first calculate the radius of the circle.
→ Diameter = 2 × Radius
→ 16 in = 2r
→ r = 16 in ÷ 2
→ r = 8 in
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Substituting values in the formula of circumference,
→ C = 2πr
→ C = (2 × π × 8) in
→ C = 16π in
<u>Therefore</u><u>,</u><u> </u><u>1</u><u>6</u><u>π</u><u> </u><u>inches</u><u> </u><u>is</u><u> </u><u>the</u><u> </u><u>required</u><u> </u><u>answer</u><u>.</u>
Answer:
1) x = 8
2) ∠RPS = 36°
Step-by-step explanation:
<u>GIVEN :-</u>
- ∠QPS = 180°
- ∠QPR = 7x + 88
- ∠RPS = 3x + 12
<u>TO FIND :-</u>
- Value of x
- Measure of ∠RPS
<u>FACTS TO KNOW BEFORE SOLVING :-</u>
In a straight line , if there are two angles such that their sum is equal to straight angle (or 180° in other words) , then those angles are known as linear pair.
<u>PROCEDURE :-</u>
1)
Measure of ∠QPS = 180° and it comprises of ∠QPR & ∠RPS.
⇒ ∠QPR & ∠RPS are linear pair.
⇒ ∠QPR + ∠RPS = 180°
⇒ 7x + 88 + 3x + 12 = 180°
⇒ 10x + 100 = 180
⇒ 10x = 180 - 100 = 80
⇒ x = 80/10 = 8
2)
x = 8. So,
∠RPS = 3×8 + 12 = 24 + 12 = 36°