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3 years ago

6

the red line in the figure is an altitude of triangle ABC. Using right angle trigonometry, write an equation involving sin C

2 answers:

andreyandreev [35.5K]3 years ago

7 0

Answer:

sinC = $\frac{h}{a}$

Step-by-step explanation:

Since the red line is an altitude then the triangles are right, thus

sinC = $\frac{opposite}{hypotenuse}$ = $\frac{h}{a}$

miv72 [106K]3 years ago

3 0

Answer:

$\Large \boxed{\mathrm{\bold{C}}}$

Step-by-step explanation:

$\sf \displaystyle sin(\theta)=\frac{opposite}{hypotenuse}$

The side opposite to $\angle C$ is h.

The hypotenuse of the smaller right triangle is a.

$\sf \displaystyle sin(C)=\frac{h}{a}$

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Answer:

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$City = 130\ miles$

Step-by-step explanation:

Given

$Highway = 31mi/gallon$

$City = 26mi/gallon$

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Required

Determine the number of miles driven on the highway and on the city

Represent the gallons used on highway with h and on city with c.

So, we have:

$c + h = 10$ ---- gallons used

and

$31h + 26c = 285$ --- distance travelled

In the first equation, make c the subject

$c = 10 - h$

Substitute 10 - h for c in the second equation

$31h + 26c = 285$

$31h + 26(10 - h) = 285$

Open bracket

$31h + 260 - 26h = 285$

Collect like terms

$31h - 26h = 285 - 260$

$5h = 25$

Make h the subject

$h = \frac{25}{5}$

$h = 5$

Substitute 5 for h in $c = 10 - h$

$c = 10 - 5$

$c = 5$

If on the highway, he travels 31 miles per gallon, then his distance on the highway is:

$Highway = 31 * 5$

$Highway = 155\ miles$

If in the highway, he travels 26 miles per gallon, then his distance on the highway is:

$City = 26 * 5$

$City = 130\ miles$

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