Question

Please help me im stuckkm

Answer 1

Answer:

Below in bold.

Step-by-step explanation:

(a) Using the Pythagoras theorem:

30^2 = 21^2 + p^2

p^2 = 30^2 - 21^2 = 459

p = √459

  = 21.4 cm to nearest tenth.

(b) cos P = 21/30 = 0.70

   m < P = 45.57 degrees to nearest hundredth.

Answer 2

Answer:

a)  p = 21.4 cm (nearest tenth)

B)  P = 45.6° (nearest tenth)

Step-by-step explanation:

As triangle PQR is a right triangle, we can use Pythagoras Theorem to find the length of p.

Pythagoras Theorem

$a^2+b^2=c^2$

where:

• a and b are the legs of the right triangle
• c is the hypotenuse (longest side) of the right triangle

From inspection of the triangle:

• a = PQ = 21
• b = QR = p
• c = PR = 30

Substitute the given values into the formula and solve for p:

$\implies 21^2+p^2=30^2$

$\implies 441+p^2=900$

$\implies 441+p^2-441=900-441$

$\implies p^2=459$

$\implies \sqrt{p^2}=\sqrt{459}$

$\implies p=\pm 3\sqrt{51}$

As p is the length, p can be positive only.

Therefore, p = 21.4 cm (nearest tenth)

To find the angle P, use the cosine trigonometric ratio.

Cosine trigonometric ratio

$\sf \cos(\theta)=\dfrac{A}{H}$

where:

• $\theta$ is the angle
• A is the side adjacent the angle
• H is the hypotenuse (the side opposite the right angle)

From inspection of the triangle:

• $\theta$ = P
• A = PQ = 21
• H = PR = 30

Substitute the given values into the formula and solve for P:

$\implies \sf \cos P=\dfrac{21}{30}$

$\implies \sf P=\cos^{-1}\left(\dfrac{21}{30}\right)$

$\implies \sf P=45.572996^{\circ}$

Therefore, the measure of angle P is 45.6° (nearest tenth).

Learn more about Pythagoras Theorem here:

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Learn more about trigonometric ratios here:

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