# Tutor profile: Graceubokmfon A.

## Questions

### Subject: Trigonometry

Given a right angle triangle pqr, with line pr as 4m, line pq as 3m and angle q as 30 degrees. Find the value of line qr and angle r.

Step 1:We are going to first identify the lines and angles; If triangle pqr is a right angle triangle, angle p = 90 degrees(one of the angles of the right angle triangle will be 90 degrees) line pr is opposite line to angle q; pr = opp line pq is adjacent line to angle q; pq = adj Step 2: Using Pythagoras theorem; which states that the square of the hypothenuse is equal to the sum of the square of the other two sides : hyp{2} = opp{2} + adj{2} this implies qr{2} = pr{2} + pq{2} This becomes qr{2} = 4{2} + 3{2} qr{2} = 16 + 9 qr{2} = 25 qr = square root of 25 therefore: line qr = 5 Step 3: We know that the total angle in a triangle is 180 degrees.. angle p + angle q + angle r = 180 if angle p is 90 degrees and angle q is 30 degrees 90 + 30 + angle r = 180 When we collect like terms(by taking the numerical terms to one side of the equality sign and the alphabetical terms to another side) angle r = 180 - 90 - 30 This implies that angle r = 60

### Subject: Geometry

1. Given that in triangle ABC angle a= 60 degrees, angle b= 90 degrees, What is the degree of angle c?

Step 1: Note: The total angle in a triangle = 180 degrees This means that angle a + angle b + angle c = 180 degrees.........equation 1 Step 2: In the question above we've been given that angle a = 60 degrees and angle b = 90 degrees,we will substitute this into equation 1 above. Equation 1 will become 60 + 90 + angles c = 180 Step 3: Collect like terms, by take all the numerical term to one side of the equation and leaving the alphabetic terms on the other side. We have angle c = 180 - 90 - 60 (note the sign of a term changes whenever it move across the equation sign) This results to angle c = 30 degrees

### Subject: Algebra

Solve 5x + 3= 7x - 1

Step 1: We solve this by collecting like terms first. (Take the terms with letters to one side of the equation, do the same thing to the terms without letters) This will become 5x - 7x= -1 -3 This implies: -2x = -4 Step 2: Divide both sides of the equation by -2 This will become x = 2

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