Question

Trigonometry help please! Find the area of the orange triangle? (Pic)?

Answer 1

Give names to all vertices of triangle.

and draw dotted line from D to E (mid point of AB )

From right angled triangle ABC

Apply Pythagorean triangle formula : AB² = AC²+BC²

But AC = BC is given

AB² = AC²+AC²

AB² = 2AC²

Substitute AB = 260

260² = 2AC²

AC² = 67600/2

AC = √33800

AC = 183.85 ft

From right angled triangle ACD

Apply Pythagorean triangle formula : AC² = AD²+CD²

183.85² = AD²+105²

AD² = 22775.8225

AD = 150.9166

From right angled triangle ADE

Apply Pythagorean triangle formula : AD² = DE²+AE²

150.9166² = DE²+(260/2)²

DE² = 150.9166² - 130²

DE² = 5875.82

DE = 76.65

Area of Orange Triangle ABD is ½(base)(height)

= ½(AB)(DE)

= ½(260)(76.65)

=  9965 square feet

Solution :

Area of Orange Triangle is 9965 square feet