Question

60 POINTS, please help me with trig.

Answer 1

Answer:

add all three angles in any triangle we get 180 degrees. So, the measure of angle A + angle B + angle C = 180 degrees. This is true for any triangle in the world of geometry. We can use this idea to find the measure of angle(s) where the degree measure is missing or not given.

Step-by-step explanation:

Answer 2

First problem: draw a line segment through the vertex R and a point C on PQ such that the segment is perpendicular to PQ, thus forming an altitude of the triangle. This new segment CR, the new segment CP, and PR form a 30-60-90 right triangle, where the measure of angle PCR is 90 degrees. CR then occurs with PR in a ratio of $\sqrt3$ to 2, so

$\dfrac{CR}{PR}=\dfrac{CR}5=\dfrac{\sqrt3}2\implies CR=\dfrac{5\sqrt3}2$

and this can be considered the height of a triangle whose base is PQ. The area is then

$\dfrac12\cdot6\cdot\dfrac{5\sqrt3}2=\dfrac{15\sqrt3}2\approx13$

Second problem: the sum of the interior angles of any triangle is 180, so the measure of the missing angle must be 180 - 20 - 35 = 125 degrees. By the law of sines, the length of the missing side (call it $x$) satisfies

$\dfrac{\sin20^\circ}9=\dfrac{\sin125^\circ}x\implies x\approx21.56$

Use Heron's formula to find the area of the triangle:

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where $A$ is the area, $a,b,c$ are the lengths of the sides, and $s=\dfrac{a+b+c}2$ is the half the perimeter of the triangle. Then the area is about $A\approx54.62$ square feet. Convert to square yards:

$54.62\text{ ft}^2\cdot\left(\dfrac{1\text{ yd}}{3\text{ ft}}\right)^2\approx6.07\text{ yd}^2$

then round up to 7 square yards. At a price of $12.50 per square yard, the total price will be $87.50.