Question

A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between the landmarks in degrees.

the triangle has
two sides(65,55)
angles (40,30)

What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.

32.5 m
42.1 m
85.1 m
98.5 m

Answer 1

The distance between the two landmarks is 98.5m

Explanation:

I've attached an image to depict where toby is standing, the landmark and the angles.

To get the distance between the 2 landmarks, we will make use of cosine rule which is given as;

c² = a² + b² − 2ab cos(C)

Where, a and b are the two given lamdmarks.

c = the distance between the landmarks

C is the angle opposite the distance between the landmarks i.e the angle at the point at where toby is standing

Now, we are not given the angle C. But we can calculate it from knowing that sum of angles in a triangle is equal to 180.since we know 2 angles, thus, C = 180 - (40 + 30) = 110°

Now, we can solve for c by plugging in the relevant values ;

c² = 55² + 65² - (2*55*65*Cos110)

c² = 4225 + 3025 -7150(-0.342)

c² = 9695.3

c=√9695.3

c=98.46m ≈ 96.5m

Answer 2

Check attachment for the included diagram

The last option is the correct otpiton 98.5m

Explanation:

We know that side 1= 65m

Side 2 =55m

Then, the angle between the two sides are not given, let call the third angle X

We know the other two opposite angles and which are 40° and 30°.

Applying sum of angle in as triangle

The sum of angle in a triangle is 180°

Then,

X+30+40 =180

X+ 70 =180

X=180-70

X=110°

So, using cosine rule

c² = a²+b²-2abCosX

c² = 65²+55²-2•65•55Cos110

c² = 4225+3025-(-2445.44)

NOTE: -×-=+

c² = 4225+3025+2445.44

c² = 9695.44

c=√9695.44

c=98.465

To the nearest ten

c= 98.5m

The last option is the correct answer