This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Here are the solutions for finding 'H' in both right-angled triangles. For the first triangle: Step 1: Identify the knowns and unknowns. We have a right-angled triangle with an angle of 30^. The side opposite this angle is H, and the side adjacent to this angle is 600. We are given 30^ = 0.5. To relate the opposite and adjacent sides, we use the tangent function: = oppositeadjacent 30^ = (H)/(600) Step 2: Calculate 30^ using the given 30^. We know that = ( )/( ). First, we find 30^ using the identity ^2 + ^2 = 1: 30^ = sqrt(1 - ^2 30^) 30^ = sqrt(1 - (0.5)^2) 30^ = sqrt(1 - 0.25) 30^ = sqrt(0.75) = sqrt((3)/(4)) = sqrt(3)2 Now, calculate 30^: 30^ = ( 30^)/( 30^) = (0.5)/(sqrt(3))2 = (1)/(2)sqrt(3)2 = (1)/(sqrt(3)) Step 3: Solve for H. Substitute the value of 30^ into the equation from Step 1: (1)/(sqrt(3)) = (H)/(600) H = (600)/(sqrt(3)) To rationalize the denominator, multiply the numerator and denominator by sqrt(3): H = 600sqrt(3)3 H = 200sqrt(3) Using the approximate value sqrt(3) ≈ 1.732: H ≈ 200 × 1.732 H ≈ 346.4 The value of H for the first triangle is 200sqrt(3) or approximately 346.4 For the second triangle: Step 1: Identify the knowns and unknowns. We have a right-angled triangle with an angle of 60^. The side opposite this angle is H, and the hypotenuse is 30 cm. We are given 60^ = 0.9. To relate the opposite side and the hypotenuse, we use the sine function: = oppositehypotenuse 60^ = (H)/(30 cm) Step 2: Solve for H. Substitute the given value of 60^ = 0.9 into the equation from Step 1: 0.9 = (H)/(30 cm) H = 0.9 × 30 cm H = 27 cm The value of H for the second triangle is 27 cm What's next?