Mountains

2. We have the same isosceles triangle ABC, with AB=AC=30cm, BC=36cm[br]Point D is on the segment AM, where M is the midpoint of the base BC, so that AD=20cm.[br][br]Requirements:[br]a) Calculate the area of the large triangle ABC.[br]b) Calculate the area of the small triangle DBC.[br]c) Find what percentage of the area of the large triangle is the area of the small triangle.

1. Consider the isosceles triangle ABC with[br]AB=AC=20cm[br]BC=24cm[br][br]Point D is on the altitude from A, so that triangle DBC is also isosceles, with DB=DC[br]D is at a distance of 12cm from line BC.[br][br]Requirement:[br]a) Determine the measure of angle ∠BAC.[br]b) Determine the measure of angle ∠BDC.

∠BAC ≈ 75.74[math]^\circ[/math][br]∠BAC = 90[math]^\circ[/math] ∠BAC ≈ 73.74[br]∠BAC = 100[math]^\circ[/math][br] ∠BAC ≈ 73.74[br]∠BAC = 90

3. Triangle ABC is isosceles with AB=AC=17cm, ∠BAC=40[br]Point D lies on the altitude from A such that triangle DBC is isosceles, with DB=DC=15cm.[br][br]Requirements:[br]a) Calculate the length of base BC.[br]b) Calculate the distance between points A and D.[br]c) Calculate the area of triangle ADC.

BC ≈ 12.6287 cm. [br]AD ≈ 8.1475 cm. [br]S[size=50]ADC[/size] ≈ 6.2432 cm[sup]2[/sup]. BC ≈ 11.6287 cm. [br]AD ≈ 2.9 cm. [br]S[size=50]ADC [/size]≈ 6.9 cm[sup]2[/sup]. BC ≈ 11.6287 cm. [br]AD ≈ 2.1475 cm. [br]S[size=50]ADC [/size]≈ 6.2432 cm[sup]2[/sup].

Mountains

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