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yaroslaw [1]
3 years ago
13

What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?

Mathematics
2 answers:
stich3 [128]3 years ago
8 0
The legs of a triangle with a hypotenuse that measures 15 units long have lengths that are equal to 15 times the sine or cosine of the given angle.
                      leg 1 = (15 units) x (cos 19) = 14.18 units
                      leg 2 = (15 units) x (sin 19) = 4.88 units
The lengths of the legs are 14.18 units and 4.88 units. 
Anarel [89]3 years ago
3 0
The side opposite the angle 19 degrees is given by 15sin 19 = 4.9 units, while the side adjacent the angle 19 degrees is given by 15cos 19 = 14.2 units.
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We conclude that the total amount accrued, principal plus interest,  from compound interest on an original principal of  $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

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Using the compound interest equation

A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

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A represents the Accrue Amount

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r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

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now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}

\:A=2500\left(1+\frac{0.05}{6}\right)^{48}

A=2500\times 1.48935      ∵  \left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935

A=\:3723.38 $

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