Question

PLS ANSWER I NEED HELPPP i have posted this question several times, i am desperate for an answer pls

right angle trigonometry

Answer 1

Explanation:

Triangle A)

use Pythagoras to find hypotenuse

c =
`\sqrt{a^(2) +b^(2) }`

c = √(
`8^(2)`+
`5^(2)`)

c= √(64+25)

c=√89

c=9.43398 mm

it's a right triangle so just find one angle using SOH CAH TOA to remember how the trig function fit on the triangle

Tan(Ф) = Opp / Adj

Ф = arcTan( 5/8)

Ф = 32.0053°

Ф = 32° approx

∠A=Ф

∠B= 180-90-32

∠B=58°

Triangle B)

∠L = 180-90-72

∠L = 18°

use CAH

Cos(Ф) = Adj / Hyp

Cos(18) =Adj / 10

10 * Cos(18) = Adj

9.51056 cm = Adj

KL = Adj

now use SOH

Sin(Ф) = Opp / Hyp

Sin(18) =Opp / 10

10* Sin(18) = Opp

3.09016 cm = Opp

KJ = Opp

Triangle C)

∠Q = 180-90-42

∠Q = 48°

CAH

Cos(∅) = Adj / Hyp

Cos(48) = 13 / Hyp

Hyp = 13 / Cos(48)

Hyp = 19.4281 km

QS = Hyp

SOH

Sin(∅) = Opp / Hyp

Sin(48) = Opp / 19.4281

19.4281 * Sin(48) = Opp

14.4379 Km = Opp

Opp = RS

Using SOH CAH TOA is super helpful to place the trig function onto a triangle :)