Solve the triangle Solve sides

Mathematics

1 answer:

Montano1993 [528]4 years ago

8 0

Answer:

Step-by-step explanation:

Triangle RST is a right angle triangle.

From the given right angle triangle

RT represents the hypotenuse of the right angle triangle.

With 26 degrees as the reference angle,

ST represents the adjacent side of the right angle triangle.

RS represents the opposite side of the right angle triangle.

1) To determine RS, we would apply trigonometric ratio

Sin θ = opposite side/hypotenuse Therefore,

Sin 26 = RS/9.1

RS = 9.1Sin26 = 9.1 × 0.4384

RS = 4.0

2) To determine ST, we would apply trigonometric ratio

Cos θ = adjacent side/hypotenuse Therefore,

Cos 26 = ST/9.1

ST = 9.1Cos26 = 9.1 × 0.8988

ST = 8.1

3) The sum of the angles in a triangle is 180 degrees. Therefore,

∠R + 26 + 90 = 180

∠R = 180 - (26 + 90)

∠R = 64 degrees

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Consider functions f and g.1 + 12f(1) = 12 + 4. – 12for * # 2 and 7 -64.2 – 16. + 1641 +48for a # -12 Which expression is equal

lisabon 2012 [21]

Given the following functions below,

$\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}\text{ and} \\ g(x)=\frac{4x^2-16x+16}{4x+48} \end{gathered}$

Factorising the denominators of both functions,

Factorising the denominator of f(x),

$\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}=\frac{x+12}{x^2+6x-2x-12}=\frac{x+12}{x(x+6)-2(x+6)}=\frac{x+12}{(x-2)(x+6)} \\ f(x)=\frac{x+12}{(x-2)(x+6)} \end{gathered}$

Factorising the denominator of g(x),

$\begin{gathered} g(x)=\frac{4x^2-16x+16}{4x+48}=\frac{4(x^2-4x+4)}{4(x+12)} \\ \text{Cancel out 4 from both numerator and denominator} \\ g(x)=\frac{x^2-4x+4}{x+12}=\frac{x^2-2x-2x+4}{x+12}=\frac{x(x-2)-2(x-2)}{x+12}=\frac{(x-2)^2}{x+12} \\ g(x)=\frac{(x-2)^2}{x+12} \end{gathered}$

Multiplying both functions,