Can some one please help me with solving this using proofs

1 answer:

8 0

$proof: \: 3(5x + 1) = 13x + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 15x + 3 = 13x + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (15x - 13x) + 3 = 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x = (5 - 3) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x = 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: x = (2 \div 2) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: x = 1$

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The right triangle shown has angles X, Y, and Z and side lengths a, b, and

laiz [17]

So attached is a picture of the triangle you are talking about and listed under are the choices:

A.) Cos Z=b/c
B.) Sin X=c/b
C.) Tan X=b/a
D.) Tan Z=a/b

The answer would then be B. SinX = c/b.

Just remember SOH CAH TOA:

Sinθ= Opposite Cosθ = Adjacent Tanθ= Opposite
Hypotenuse Hypotenuse Adjacent

Using the triangle in the scenario, you just need to identify which side is which.

Given m∠Z
Adjacent = b
Opposite = a
Hypotenuse = c

SinZ= a CosZ = b TanZ= a
c c b

Given m∠X:

Adjacent = b
Opposite = a
Hypotenuse = c

SinX= b CosX = a TanX= b 
c c a

So the answer is B.

Attached is a picture of how I assigned the sides depending on the angle used.