Jas A.

Chemistry and Spanish Major, bartender by night

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Pre-Calculus

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Question:

Given a vector <-3,-4>, find its unit vector.

Jas A.

Answer:

A Unit Vector maintains direction of the original vector, with a magnitude of 1. Begin by solving for the magnitude of the vector given: We are given the vector <-3,-4> magnitude = $$ \sqrt{(-3)^{2}+(-4)^{2}} $$ =$$ \sqrt{9+16} $$ =$$ \sqrt{25} $$ =5 To find the unit vector, make the magnitude of the given vector 1. To do this, we divide the magnitude by itself $$ \frac{5}{5} $$=1 Now we must also divide each of the components of the given vector by 5. Answer: <$$ \frac{-3}{5} $$,$$ \frac{-4}{5} $$>

Trigonometry

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Question:

Given a triangle ABC, where angle A=62*, angle B=31*, and side length c=4cm, complete the triangle. Summarize your answer in one place at the end. Round your answers to the nearest hundredth.

Jas A.

Answer:

We want to complete the triangle, meaning we want to solve for all missing lengths and angles. Begin by finding the last angle of the triangle: 180*-62*-31*= 87*. Angle C=87*. Using the Law of Sines, set up your proportion to find the remaining side lengths. We will solve for side length a first: $$ \frac{4cm}{sin(87*)} $$ = $$ \frac{a}{sin(62*)} $$ Multiply both sides by sin(62*) to get a by itself: a = $$ \frac{4sin(62*)}{sin(87*)} $$ a = 3.54 cm Repeat these steps using the Law of Sines to solve for side length b. Angle A=62* Angle B=31* Angle C=87* side a=3.54 cm side b=2.06 cm side c=4 cm

Geometry

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Question:

Given a right triangle ABC with side AB=24ft and hypotenuse, side AC=74ft, Find the length of the missing side BC.

Jas A.

Answer:

BC=70ft

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