Question

PLZ HELP, WORTH 20 PTS.

Determine the approximate value of t.


2.03

5.54

6.4

15.45

Answer 1

B. 5.54

Explanation:

To find out what t is, use the formula t=√[r² + s² - 2rs * cos(T)].

t = √[4² + 5² - 2(4(5)) * cos(75)]

t = √[16 + 25 - 8(5) * cos(75)]

t = √[41 - 40 * cos(75)] (For convenience, 40 * cos(75) has been approximated.

t = √[41 - 10]

t = √31

To approximate a square root subtract the lower square (25) from 31 and put that over the higher square (36) minus the lower square (25).

t ≈ 5 + (31 - 25)/(36 - 25)

t ≈ 5 + 6/11

t ≈ 5 6/11 ≈ 5.54, so B is the answer.

Answer 2

The approximate value for t is 5.54

Answer: Option B

Explanation:

The law of cosines generalizes the Pythagorean formula to all triangles. It says that
`c^(2)`, the square of one side of the triangle, is equal to
`a^(2)+b^(2)` product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

`c^(2)=a^(2)+b^(2)-2 a b \cos C`

According to the given triangle in figure, the values are

a = 5

b = 4

c = t

`\cos C=\cos 75^(\circ)=0.2588`

Substituting all the given values in the formula, we get

`t^(2)=5^(2)+4-(2 * 5 * 4 * 0.2588)`

`t^(2)=25+16-10.3527`

`t^(2)=41-10.3527=30.647`

Taking square roots, we get the value for ‘t’ as below,

`t=√(30.647)`

t = 5.536 (approximately 5.54)