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spayn [35]
3 years ago
13

What is the value of r? Round your final answer to the nearest whole number.

Mathematics
2 answers:
vaieri [72.5K]3 years ago
8 0

Answer:

r = 13

Step-by-step explanation:

Hypotenuse is the side opposite to 90 degree angle, so hypotenuse is r.

Also, with respect to the angle given, the side "12" is the opposite.

So we have opposite side to angle and we need hypotenuse. Which trigonometric ratio related opposite with hypotenuse? It is SINE.

So we can write:

Sin(67.4)=\frac{Opposite}{Hypotenuse}=\frac{12}{r}\\rSin(67.4)=12\\r=\frac{12}{Sin(67.4)}\\r=12.99

Rounded to nearest whole number, r = 13

Len [333]3 years ago
6 0

<u>Answer:</u>

r = 13

<u>Step-by-step explanation:</u>

We are given a right angled triangle with one known angle and two side lengths (12 and r) and we are to find the value of r (which is the hypotenuse).

For that, we can use sine.

sin ( 67.4 ) = \frac {12} {r}

0.923 = \frac {12} {r}

r = \frac {12} {0.923}

r = 12.9

r ≈ 13

Therefore, the value of r is 13.

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A basketball gymnasium is 25 meters high, 80 meters wide and 200 meters long. We want to connect two strings, one from each of t
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Answer:

a) the centre is at (12.5 m, 40 m , 100 m ) with respect to our position

b) the length of the strings S will be 216.85 m

c) the angle that is formed by the strings is  1.23 rad

Step-by-step explanation:

assuming that we stand on one of the corners on the floor , so our coordinates are (0,0,0)  , then the coordinates of the center of the gymnasium   are found through

x center = (25 + 0)/2 = 12.5 m

y center = (80+ 0)/2 = 40 m

z center = (200+ 0)/2 = 100 m

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c) the angle can be found through the dot product of the vectors that represent the strings S₁ and S₂

S₁ =(25,80,10)

S₂ =(-25,80,100)

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S₁*S₂ = 25*(-25) +80*80 + 100*100 = 15775

but also

S₁*S₂ = |S₁||S₂| cos θ = |S|² * cos θ

S₁*S₂ =  |S|² * cos θ

cos θ= S₁*S₂/|S|²

θ= cos ⁻¹ ( S₁*S₂/|S|² ) = cos ⁻¹ [15775/(25²+80²+200²)] = 1.23 rad

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