Answers
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:
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
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleFrom inspection of the triangle:
a = PQ = 21b = QR = pc = PR = 30Substitute the given values into the formula and solve for p:
[tex]\implies 21^2+p^2=30^2[/tex]
[tex]\implies 441+p^2=900[/tex]
[tex]\implies 441+p^2-441=900-441[/tex]
[tex]\implies p^2=459[/tex]
[tex]\implies \sqrt{p^2}=\sqrt{459}[/tex]
[tex]\implies p=\pm 3\sqrt{51}[/tex]
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
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)From inspection of the triangle:
[tex]\theta[/tex] = PA = PQ = 21H = PR = 30Substitute the given values into the formula and solve for P:
[tex]\implies \sf \cos P=\dfrac{21}{30}[/tex]
[tex]\implies \sf P=\cos^{-1}\left(\dfrac{21}{30}\right)[/tex]
[tex]\implies \sf P=45.572996^{\circ}[/tex]
Therefore, the measure of angle P is 45.6° (nearest tenth).
Learn more about Pythagoras Theorem here:
https://brainly.com/question/27648540
Learn more about trigonometric ratios here:
https://brainly.com/question/26861422
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Step-by-step explanation:
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What is a translation?The process of changing the location of the image on the coordinate system will be known as the translation. A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
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Therefore, the image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
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Answers
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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