Question

PLZ HELP, WORTH 20 PTS.

Answer 1

The approximate value for t is 5.54

Answer: Option B

Step-by-step 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

          $t^{2}=5^{2}+4-(2 \times 5 \times 4 \times 0.2588)$

          $t^{2}=25+16-10.3527$

          $t^{2}=41-10.3527=30.647$

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

                             $t=\sqrt{30.647}$

                             t = 5.536 (approximately 5.54)