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2 years ago

The diagram shows a right-angled triangle.

Mathematics

1 answer:

amm18122 years ago

4 0

The length of the hypotenuse and the opposite side to angle x of the right triangle are 8 cm and 3 cm respectively, which gives angle x as approximately 22.0°

<h3>Which of the trigonometric ratios can be used to find x°?</h3>

A description of the parts of the triangle are;

Length of the hypotenuse side = 8 cm

Length of the opposite side to x° = 3 cm

The trigonometric ratio of the sine of x° is presented as follows;

$sin(x) = \frac{Opposite}{Hypotenuse}$

Therefore;

$sin(x) = \frac{3}{8}$

Which gives;

${x}^{ \circ} = arcsine \left( \frac{3}{8} \right) \approx {22.0}^{ \circ}$

Angle x ≈ 22.0°

Learn more about trigonometric ratios of the cosine, sines, and tangent of angles here:

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Rachel has developed a plan to start paying off her credit card debt, and has stopped making purchases with her credit card. She

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Present value of annuity PV = P(1 - (1 + r/t)^-nt) / (r/t)
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HELP Use either law of sines or law of cosine. Need help on this problem! show work please!

Marina86 [1]

Answer: x = 15.035677095729 approximately

Round this however you need to.

=================================================

Explanation:

I'm assuming you want to find the value of x, which your diagram is showing to be the length of segment QR.

If so, then we'll need to find the measure of angle Q first. Using the law of sines, we get the following:

sin(Q)/q = sin(R)/r

sin(Q)/PR = sin(R)/PQ

sin(Q)/13 = sin(85)/19

sin(Q) = 13*sin(85)/19

sin(Q) = 0.6816068987

Q = arcsin(0.6816068987) ... or ... Q = 180-arcsin(0.6816068987)

Q = 42.9693397461 ... or ... Q = 137.0306602539

These values are approximate.

----------------

Now if Q = 42.9693397461 approximately, then angle P is

P = 180-Q-R

P = 180-42.9693397461-85

P = 52.0306602539

Similarly, if Q = 137.0306602539 approximately, then,

P = 180-Q-R

P = 180-137.0306602539-85

P = -42.0306602539

A negative angle is not possible, so we'll ignore Q = 137.0306602539

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The only possible value of angle P is approximately P = 52.0306602539

Let's apply the law of sines again to find side p, aka segment QR

sin(P)/p = sin(R)/r

sin(P)/QR = sin(R)/PQ

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19*sin(52.0306602539) = x*sin(85)

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