What is X? How do you know?

Mathematics

1 answer:

natka813 [3]3 years ago

8 0

The sides of a right triangle are related by trig functions of the acute angles. The relationships are described by the mnemonic SOH CAH TOA. The meaning of this is
.. Sin = Opposite/Hypotenuse
.. Cos = Adjacent/Hypotenuse
.. Tan = Opposite/Adjacent

Here, you are given the adjacent side and the hypotenuse for the angle. This means you can use the relation
.. Cos = Adjacent/Hypotenuse

Putting in the given information lets you find x.
.. cos(22°) = x/11
.. 11*cos(22°) = x ≈ 10.199

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What is the value of x with clear working out please?

nirvana33 [79]

Answer:

Answer:  x is 46° 

Step-by-step explanation:

• Let's first find Angle ACB

${ \rm{ \angle ACB + 23 \degree + 90 \degree = 180 \degree}} \\ \\ { \rm{ \angle ACB = (180 - 90 - 23) \degree}} \\ \\ { \underline{ \rm{ \: \angle ACB = 67 \degree}}}$

• From alternative angles, x = Angle BAC.

• Since AB = AC, then Angle ABC = Angle ACB

${ \rm{x + \angle ABC + \angle ACB = 180 \degree}} \\ \\ { \rm{x + 67 \degree + 67 \degree = 180 \degree}} \\ \\ { \rm{x + 134 \degree = 180 \degree}} \\ \\ { \boxed{ \rm{x = 46 \degree}}}$