Answer:
9. 149 degrees
10. 2 units
Step-by-step explanation:
9. These two triangles are congruent, which means their corresponding side lengths and angles are are equal.
Here, the angle on the bottom triangle marked x actually corresponds to the angle in the top triangle that is unlabelled. That means if we find the unlabelled angle in the top triangle, we've found x.
All angles of a triangle add up to 180, so we can write: x + 17 + 14 = 180
Solve for x: x = 180 - 17 - 14 = 149 degrees
10. Similar triangles have their corresponding angles the same and their corresponding sides in the same <em>ratio</em>, not the same length this time.
Notice that RP is the long leg of triangle PQR and that AC is the long leg of triangle ABC, which means that they correspond to each other and we can write the ratio: RP / AC = 16 / x.
Notice that QP is the short leg of triangle PQR and that AB is the short leg of triangle ABC, which means that they correspond to each other and we can write the ratio: QP / AB = 8 / 1.
Now we can set these two ratios equal and solve for x:
16/x = 8/1
8x = 16
x = 2 units
Answer: B. 5/13
This is the same as writing
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Reason:
We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.
a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse
The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.
Now we can compute sine of theta
This points us to choice B as the final answer.
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Extra Info (optional)
- 5/12 is the value of tan(theta) since it's opposite/adjacent
- 12/5 is the value of cot(theta), the reciprocal of tangent
- 12/13 is the value of cos(theta), because cos = adjacent/hypotenuse
Let x be the number of pages of advertisements.
Write a proportion from the table:
of a page of advertisment - 5 pages in a magazine
x pages of advertisment - 98 pages in a magazine,
then
Find x:
Answer: 13 whole pages and of 14th page are advertisments, so 14 pages contain advertisments.