Find the area of triangle ABC. Give your answer correct to 1 decimal place AC=7 Cb=12 a=72 degrees b=59 degrees

Mathematics

1 answer:

Tems11 [23]3 years ago

3 0

Answer:

31.7 cm²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = $\frac{1}{2}$ absinC

where a, b are the 2 sides given and C the angle between them

∠ C = 180° - (72 + 59)° = 180° - 131° = 49° , thus

A = 0.5 × 12 × 7 × sin49° ≈ 31.7 cm² ( to 1 dec. place )

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$\large\begin{array}{l} \textsf{Restrictions for the domain:}\\\\ \bullet~~\textsf{Denominators must not be zero:}\\\\ \mathsf{(x+7)(x-7)\ne 0}\\\\ \begin{array}{rcl} \mathsf{x+7\ne 0}&~\textsf{ and }~&\mathsf{x-7\ne 0}\\\\ \mathsf{x\ne -7}&~\textsf{ and }~&\mathsf{x\ne 7} \end{array} \end{array}$

$\large\begin{array}{l} \textsf{Therefore, the domain of f is}\\\\ \mathsf{D_f=\{x\in\mathbb{R}:~~x\ne -7~~and~~x\ne 7\}}\\\\\\ \textsf{or using a more compact form}\\\\ \mathsf{D_f=\mathbb{R}\setminus\{-7,\,7\}}\\\\\\ \textsf{or using the interval notation}\\\\ \mathsf{D_f=\left]-\infty,\,-7\right[\,\cup\,\left]7,\,+\infty\right[.} \end{array}$

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$\large\textsf{I hope it helps. :-)}$

Tags: function domain real rational factorizing special product interval

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