Find the perimeter of rectangle PQRS with vertices P(0,0), Q(0,7), R(12,7) & S (12,0)

Use the law of Sines to find the missing angle of the triangle. <br> Find m

Whitepunk [10]

Ah...Trigonometry is fun!

The law of sines states:
$\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}$
The transitive property (switching the orders of the equations) applies here. Therfore, we can say that $\frac{sinA}{a}=\frac{sinC}{c}$

We then plug in our given values to find C

$\frac{sin24}{77}=\frac{sinC}{162}$
$\frac{162*sin24}{77}=sinC$
Solving, we get 0.8557316387. We're not done yet!

We are trying to find an angle measure, so we'll do the inverse of the ratio we used (sin).

arcsin0.8557316387 (arcsin is the same as inverse sin)
=58.8 (approximate)

So the measure of angle C is 58.8. You could check this by reinserting it into the equation $\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}$ .

:)

6 0

3 years ago

7% of 120 (Need work shown)

inessss [21]

1% of 120 is 1.2, so 7 *1.2 = 8.4

Also you could set up the proportion 7/100 = x/120 and solve for x.

3 0

2 years ago

Read 2 more answers

Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms: