**TASK 1**

===========================================================

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**

===========================================================

**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**

===========================================================

**Question 1**

**Analysis:**

- 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.

A visual representation would be much appreciation. Please include a diagram.

ReplyDeleteYou did not really specify assumptions. What are your assumption.

ReplyDeleteYou did not specify who/what A and B are. Do they represent the 2 men?

You can add some pictures to illustrate what you are talking about. Especially for the last assumption where you stated that there are infinite answers. Why are there infinite answers?

Working is very concise and easy to understand.

- Group 4 (Mason, Kai En, Crystal, Wai Kit, Farrell)