Mathematics, 09.07.2019 13:10 ghari112345

Find the longer leg of the triangle.
a. 3
b. $\sqrt{3}$
c. 9
d. $\sqrt{6}$

$Find the longer leg of the triangle. a. 3 b. [tex]\sqrt{3}[/tex]$

Answers: 2

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Answer from: floydsidney1119

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given. The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship $\sin{\theta} < \cos{\theta}$ holds for all acute angles? (That is, $0^{\circ} < \theta$ ?) It turns out that:

$\sin{\theta} < \cos{\theta}$ if $0^{\circ} < \theta$ ; $\sin{\theta} \cos{\theta}$ if $45^{\circ} < \theta$ ; $\sin{\theta} = \cos{\theta}$ if $\theta = 45^{\circ}$ .

Answer from: Parmenter

Step-by-step explanation:

Since the triangle is right use the cosine ratio

cos30° = $\frac{adjacent }{hypotenuse}$ = $\frac{adj}{2\sqrt{3} }$ , so

$\frac{\sqrt{3} }{2}$ = $\frac{adj}{2\sqrt{3} }$

Multiply both sides by 2 $\sqrt{3}$

adj = $\frac{\sqrt{3} }{2}$ × 2 $\sqrt{3}$ = 3

Answer from: Quest

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6 = 0.00000180

1.80 x 10-4 = 0.000180 (bigger, or "less small", than the former one)

1.8 x 10-2 = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

Answer from: Quest

180° is the answer from the equation