Use trigonometry to solve the triangle shown. Round all side lengths to one decimal place and all angle measures to the nearest whole degree.

Answer/Step-by-step explanation:

Recall: SOH CAH TOA

✔️Find <A:

Reference angle (θ) = A

Opposite side = 14 cm

Hypotenuse = 20 cm

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin A = 14/20

A =

m<A = 44° (nearest whole number)

✔️Find <C:

Reference angle (θ) = C

Adjacent side = 14 cm

Hypotenuse = 20 cm

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos C = 14/20

C =

m<C = 46° (nearest whole number)

✔️Find AB:

Reference angle (θ) = C = 46°

Opposite side = AB

Hypotenuse = 20 cm

Apply SOH:

Sin θ = Opp/Hyp

Sin 46° = AB/20

20*Sin 46° = AB

AB = 14.4 cm (one decimal place)

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!