Question

Pleas help me solve #1 :( Your answer helps so much!!

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trig. ratios in the right triangle and

tan45° = 1, sin45° = $\frac{1}{\sqrt{2} }$, then

tan45° = $\frac{opposite}{adjacent}$ = $\frac{7}{x}$

Multiply both sides by x

x × 1 = 7 ⇒ x = 7

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sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{7}{y}$

Multiply both sides by y

y × sin45° = 7 ( divide both sides by sin 45° )

y = 7 / sin45° = 7 / 1/$\sqrt{2}$ = 7$\sqrt{2}$

Answer 2

ANSWER

$y = 7 \sqrt{2}$

$x = 7$

EXPLANATION

The given triangle has a right angle.

The side opposite to the 45° angle is 7 units.

To find angle x, we use the tangent ratio.

Recall the mnemonics TOA, which means,

$\tan(45 \degree) = \frac{opposite}{adjacent}$

$\tan(45 \degree) = \frac{7}{x}$

$1 = \frac{7}{x}$

$x = 7$

To find y, we use the sine ratio, which means

$\sin(45 \degree) = \frac{opposite}{hypotenuse}$

$\sin(45 \degree) = \frac{7}{y}$

$y= \frac{7}{\sin(45 \degree) }$

$y= \frac{7}{ \frac{1}{ \sqrt{2} } }$

$y = 7 \times \frac{ \sqrt{2} }{1}$

$y = 7 \sqrt{2}$