Question: 3. In the triangle ABC, ∠B=90∘, ∠C=26.35∘ and \(b…
In the triangle ABC, ∠B=90∘, ∠C=26.35∘ and b=13.4 cm. Calculate the length of side c of the triangle.
In the triangle ABC, ∠C=90∘, ∠A=69.3∘ and a=3.4 cm. Calculate the length of side c of the triangle.
An equilateral triangle has a vertical height of 20 cm. Calculate the length of the equal sides.
Calculate the length of the equal sides of an isosceles triangle whose altitude (vertical height) is 15 cm and whose equal angles are 48.6∘.
Solution
Problem 3 In triangle ABC, we are given: - ∠B=90∘ - ∠C=26.35∘ - b=13.4cm We need to find the length of side c. First, let’s find ∠A: ∠A=180∘−∠B−∠C∠A=180∘−90∘−26.35∘=63.65∘ Using the sine function in right-angled triangle ABC: sin∠Ac=sin∠Cbc=sin∠Cb⋅sin∠Ac=sin26.35∘13.4⋅sin63.65∘ Calculating the values: sin63.65∘≈0.894sin26.35∘≈0.446c=0.44613.4⋅0.894≈26.9cmAnswer:c≈26.9cm --- Problem 4 In triangle ABC, we are given: - ∠C=90∘ - ∠A=69.3∘ - a=3.4cm We need to find the length of side c. First, find ∠B: ∠B=180∘−∠A−∠C∠B=180∘−69.3∘−90∘=20.7∘ Using the sine function: sin∠Ac=sin∠Cac=sin∠Ca⋅sin∠Ac=sin90∘3.4⋅sin69.3∘ Calculating the values: sin69.3∘≈0.939sin90∘=1c=13.4⋅0.939≈3.2cmAnswer:c≈3.2cm --- Problem 5 In an equilateral triangle, the vertical height (h) is given as 20cm. We need to find the length of the equal sides. In an equilateral triangle: h=23⋅side Let s be the length of the side: 20=23⋅ss=320×2s=340=3403≈23.1cmAnswer: The equal sides are approximately 23.1cm long. --- Problem 6 In an isosceles triangle, the altitude (h) is 15cm, and the equal angles are 48.6∘. We need to find the length of the equal sides. Let s be the length of the equal sides. The altitude divides the isosceles triangle into two congruent right-angled triangles, each with: - An angle of 48.6∘ - Opposite side (altitude) = 15cm Using the sine function: sin48.6∘=shs=sin48.6∘hs=sin48.6∘15 Calculating the value: sin48.6∘≈0.750s=0.75015=20cmAnswer: The equal sides are 20cm long.