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Subject Test Math 2

Question 8 of 28

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SAT Subject Test

The figure shows triangle A B C. The length of side A C is labeled x and the length of side B C is labeled 10.

Note: Figure not drawn to scale.

In the figure above, A B equals B C and the measure of angle C is 40 to the power of ring operator end exponent. What is the value of x?

Select an Answer

6.5

Correct Answer: 
No

6.8

Correct Answer: 
No

14.7

Correct Answer: 
No

15.3

Correct Answer: 
Yes

234.7

Correct Answer: 
No

There are several ways to solve this problem. One way is to use the law of sines. Since A B equals B C, the measure ofangle A is 40 to the power of ring operator end exponent and the measure of angle B is 100 to the power of ring operator end exponent. Thus, fraction numerator 10 over denominator sin function application 40 to the power of ring operator end exponent end fraction equals fraction numerator x over denominator sin invisible times 100 to the power of ring operator end exponent function application end fraction and x equals 15.3. (Make sure your calculator is in degree mode.)

You can also use the law of cosines:

c to the power of 2 end exponent equals a to the power of 2 end exponent plus b to the power of 2 end exponent minus 2 a b invisible times cos function application C

x to the power of 2 end exponent equals 10 to the power of 2 end exponent plus 10 to the power of 2 end exponent minus 2 left parenthesis 10 right parenthesis left parenthesis 10 right parenthesis cos function application 100 to the power of ring operator end exponent

x to the power of 2 end exponent equals 234.7296

x equals 15.3

Since straight capital delta A B C is isosceles, you can draw the altitude to the triangle.

The figure shows triangle A B C with horizontal side A C and vertex B above side A C. The length of side A B and the length of side B C are both labeled 10. Angle C is labeled 40 degrees. A vertical line segment is drawn from vertex B to side A C. The vertical line segment intersects side A C at a right angle, and the distance between the point of intersection and vertex C is labeled x over 2.

cos function application 40 to the power of ring operator end exponent equals fraction numerator fraction numerator x over denominator 2 end fraction over denominator 10 end fraction

7.66 equals fraction numerator 1 over denominator 2 end fraction x

15.32 equals x

Question Difficulty: 
medium