Question

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

Answer 1

see explanation

Explanation:

Using the trig. ratios in the right triangle and

tan45° = 1, sin45° =
`(1)/(√(2) )`, then

tan45° =
`(opposite)/(adjacent)` =
`(7)/(x)`

Multiply both sides by x

x × 1 = 7 ⇒ x = 7

---------------------------------------

sin45° =
`(opposite)/(hypotenuse)` =
`(7)/(y)`

Multiply both sides by y

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

y = 7 / sin45° = 7 / 1/
`√(2)` = 7
`√(2)`

Answer 2

`y = 7 √(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) = (opposite)/(adjacent)`

`\tan(45 \degree) = (7)/(x)`

`1 = (7)/(x)`

`x = 7`

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

`\sin(45 \degree) = (opposite)/(hypotenuse)`

`\sin(45 \degree) = (7)/(y)`

`y= (7)/(\sin(45 \degree) )`

`y= (7)/( (1)/( √(2) ) )`

`y = 7 * ( √(2) )/(1)`

`y = 7 √(2)`