Sum

ΔAMT∼ΔAHE, construct Δ AMT such that MA = 6.3 cm, ∠MAT=120°, AT = 4.9 cm and `"MA"/"HA"=7/5`, then construct ΔAHE.

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#### Solution

Δ AMT and Δ AHE are give

⇒ `("MA")/("HA")= ("AT")/("AE") =("TM")/("EH")=7/5`

⇒ `("MA")/("HA")=7/5 ⇒ 6.3/"HA" =7/5`

⇒ `"HA" =(6.3xx5)/7`

⇒ HA = 4.5cm

Similarly, `"AT"/"AE" =7/5`

⇒ `4.9/"AE" =7/5 ⇒"AE" =(4.9xx5)/7⇒"AE"=3.5`cm

Given triangle Required triangle

Steps of Constructing the required triangle:

1. Draw a line segment of some length HP and mark an arc of 4.5cm(as calculated above) and name it as A.

2. At vertex A, make an angle of 120°

3. Mark an arc of 3.5cm (as calculated above) on AT’ and name it E.

4. Join HE.

5. Δ AHE is the required triangle.

Concept: Application of Trigonometry

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