Solve for the variable when the hypotinuse is 10 and you know one angle, 42

The other sides are 6.7 units and 7.4 units

Step-by-step explanation: Every right angled triangle can be solved by use of the trigonometric ratios. We can use the sine, cosine or tangent depending on which sides are given. If one angle has been given as 42 degrees, then the side opposite that angle can be calculated as,

Sin 42 = opposite/hypotenuse

Sin 42 = a/10

We cross multiply and we now have

Sin42 x 10 = a

0.6691 x 10 = a

a = 6.69 (which is approximately 6.7)

If one of the other two angles was given as 42, then the third angle would be calculated as 180 - (90 + 42) {sum of angles in a triangle equals 180} and that equals 48.

To calculate the third side,

Sin48 = opposite/hypotenuse

Sin48 = y/10

We cross multiply and we have

Sin48 x 10 = y

0.7431 x 10 = y

y = 7.43 (which is approximately 7.4)

Therefore the two other sides are 6.7 and 7.4

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have