one leg of a right triangle is 28 centimeters long, and the other leg is 14 centimeters long. what is the…
one leg of a right triangle is 28 centimeters long, and the other leg is 14 centimeters long. what is the length of the hypotenuse?\n31 cm\n154 cm\n42 cm\n6 cm\nquestion 12 = multiple choice question\npoints 1\na force of 89 n is exerted 28° north of east. what is the eastward component of this force?\nx = 125(tan(30°))\nx = 89(cos(28°))\nx = 28(cos(89°))\nx = 28(tan(89°))
Answer
Explanation:
Step1: Recall Pythagorean theorem
For a right - triangle with legs (a) and (b) and hypotenuse (c), (c^{2}=a^{2}+b^{2}). Here (a = 28) cm and (b = 14) cm. [c^{2}=28^{2}+14^{2}] [c^{2}=784 + 196] [c^{2}=980]
Step2: Calculate (c)
[c=\sqrt{980}=\sqrt{196\times5}=14\sqrt{5}\approx31] cm
Step3: Analyze force - component problem
If a force (F) is exerted at an angle (\theta) with respect to the x - axis (east - west axis), the x - component (eastward component) of the force is given by (F_x=F\cos\theta). Here (F = 89) N and (\theta = 28^{\circ}), so (F_x=89\cos(28^{\circ}))
Answer:
Question 11: 31 cm Question 12: (x = 89(\cos(28^{\circ})))