Point P is outside a circle with center O and is 10 cm from the center. The circle has a radius of 5 cm. Lines PA and PB are two
1 answer:
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Answer:
- ∠PAO = 90°
- ∠APO = 30°
- ∠AOB = 120°
- PB ≈ 8.7
Step-by-step explanation:
A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.
OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.
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As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.
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SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Step-by-step explanation:
Given :
At the state fair, admission at the gate is $9.
In addition, the cost of each ride is $3.
Suppose that Sam will go on x rides.
Then, cost of x rides ( in dollars) = Cost per ride x Number of rides
=3x
Total cost ( in dollars) : Admission fee + cost of x rides
= 9+3x
Sam wants the total number of dollars he spends on admission and rides to be at most t ( less than or equal to t )
CONCLUSION:
The final answer is:
Using the values and variables given, write an inequality describing this.
