Group 1 (Shaun, Desiree, Owen, Ryan)

TASK 1

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Two men facing a tall building notice the angle of elevation to the top of the building to be 30^o and 60^o respectively. If the height of the building is known to be h =120 m, find the distance (in meters) between the two men.

Assumptions:
Building's area is negligible
The men are of the same height
They are looking from their feet

Assuming A and B are on the same side of the building.

tan(30) = 120/A

A = 120/tan(30)

tan(60) = 120/B

B = 120/tan(60)

Dif between A and B = 120/tan(30) - 120/tan(60)

= 139m (3sf) 

Assuming A and B are on different sides of the building

Dif between A and B = 120/tan(30) + 120/tan(60)

= 277m (3sf) 

Assuming A and B are perpendicular to each other

Dif between A and B = Squareroot ((120/tan(30))^2 + (120/tan(60))^2)

= 219m (3sf)

Assuming A and B and building do not lie on the same plane

Infinite answers that are impossible to find.

TASK 2

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Sine Rule Explanation

Step 1: Divide triangle ABC into two parts, with a straight line intersecting C and forming a right angle at the intersection with line AB

Step 2: Deduce SinA and SinB, which is opposite/hypotenuse, which is h/b and h/a respectively.

Step 3: Express each equation as a subject of h, forming h= SinAb and h= SinBa

Step 4: SinAb = SinBa , since h = h

Step 5: SinA = (SinBa)/b , bring b over to right side

Step 6: SinA/a = SinB/b , bring a over to left side

Step 7: Hence, SinA/a = SinB/b = SinC/c

Cosine rule explanation

Step 1: CosA = x/b, then make x the subject to be substituted later, which is x = bCosA

Step 2: Use pythagora's theorem on both the left and right hand side right angle triangle.

Left: a^2 = (c-x)^2 + h^2

a^2 = c^2 - 2cx +x^2 + h^2

x^2 + h^2 = 2cx - c^2 + a^2

Right: b^2 = h^2 + x^2

Step 3: Sub right into left

b^2 = 2cx - c^2 + a^2

Step 4: Sub step 1 x into the equation

b^2 = 2bc(cosA) - c^2 + a^2

Step 5: Rearrange the equation

b^2 + c^2 - a^2 = 2bc(CosA)

CosA = (b^2 + c^2 - a^2) / 2bc

By interchanging B and C, we will get similar equations

CosB = (a^2 + c^2 - b^2) / 2ac

CosC = (a^2 + b^2 - c^2) / 2ab

TASK 3

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Question 1 

Analysis:

1. Analysis of suitability of solution

The answer is 875m which is a suitable as a length of the triangle as it it not too large or small a value. (It is not negative or much larger, e.g. 5 digit figure)

Through the use of a diagram we are able to view the problem in a clearer way and have used Cosine rule to deduce the answer, the values used in the Cosine rule is mostly given in the question, and Cosine rule is a valid way of solving the problem and can be used for any triangle.