Respuesta :
Answer:
The length of QR to the nearest tenth of a foot is 287.28 feet.
Step-by-step explanation:
Let a right angled Triangle QRS have base SQ, perpendicular RS and Hypotenuse QR.
∠S = 90°
∠Q = 17°
Perpendicular = 84 ft
We know that for a right angle triangle
SinΘ = perpendicular/Hypotenuse
Sin ∠Q = 84/QR
QR = 84/sin(17°)
QR = 84/0.2924
QR = 287.2777
QR = 287.28 feet
The cosine rule is used to determine the length of side q. Then the length of side q is 5.34 inches.
What is trigonometry?
Trigonometry deals with the relationship between the sides and angles of a triangle.
In ΔQRS, r = 5.1 inches, s = 2.4 inches and ∠Q=26°.
Then the length of q will be given by the cosine rule.
[tex]\rm q = \sqrt{r^2 + s^2 - 2rs \cos Q}\\\\q = \sqrt{5.1^2 + 2.4^2 - 2 \times 5.1 \times 2.4 \cos 26^o}\\\\q = \sqrt{26.01 + 5.76 - 24.48 \times 0.89879}\\\\q = \sqrt{50.49 - 22}\\\\q = \sqrt{28.49}\\\\q = 5.34 \ inches[/tex]
The length of the q is 5.34 inches.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
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