Question

Two farmers each have triangular plots of land in the diagram below with approximate values shown for lengths in feet

Answer 1

• a) Plots are similar
• b) x= 5577 feet

Explanation:

Refer to attached

Question

• a) Are the plots of land similar?
• b) Find to the exact value of x and rounded to the nearest tenth?

Solution

The small triangle have missing angle of 180° - (52° + 58°) = 70°

This is indicating both triangles have same 3 angle measures.

Since all angles are same, the triangles are similar.

Corresponding sides, against corresponding angles are:

• 6180 and 8240
• x and 7436

As per property of similarity, the ratio of corresponding sides is same

• 6180/8240 = x/7436
• x = 6180*7436/8240
• x = 5577 feet