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densk [106]
3 years ago
10

In triangle STU, u2 = s2 + t2.

Mathematics
1 answer:
sineoko [7]3 years ago
3 0

Answer:

(B) The measure of angle SUT is equal to 90 degrees

Step-by-step explanation:

It is given that in In triangle STU, u^2=s^2+t^2.

We can see from the triangle and also the given condition that the triangle will be right triangle as it is satisfying the Pythagoras theorem.

(Hyp)^2=(Base)^2+(Perpendicular)^2

that is:

u^{2}=s^{2}+t^{2}

where u is the hypotenuse, s is the base and t is the perpendicular.

Thus, the angle SUT should be of 90°.

Thus, The measure of angle SUT is equal to 90 degrees.

Hence, option B is correct.

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Step-by-step explanation:

Please find the attachment.

Let L be the length of the ramp in feet.  

We have been given that steel loading ramps are used to load a lawn mower onto a truck bed 37.5 inches above the ground. The ramp make a 30° angle with the ground.

We can see from our attachment that ramp and truck bed forms a right triangle with ground. The truck bed is opposite side and length of ramp is hypotenuse of our given angle.

Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use Sine to solve for L.

\text{Sine}=\frac{\text{Opposite}}{\text{Hypotenuse}}

Upon substituting our given values in above formula we will get,

\text{Sin(30)}=\frac{37.5}{L}

L=\frac{37.5}{\text{Sin(30)}}

L=\frac{37.5}{0.5}

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Therefore, the length of the ramp is 75 inches.

Let us convert the length of ramp in feet.

1 feet = 12 inches.

\text{75 inches}=\frac{75\text{ inches}}{\frac{12\text{ inches}}{\text{feet}}}

\text{75 inches}=\frac{75\text{ inches}}{12}\times \frac{\text{ feet}}{\text{inches}}

\text{75 inches}=\frac{75}{12}\times\text{ feet}

\text{75 inches}=6.25\text{ feet}

Therefore, the length of the ramp is 6.25 feet.

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