Ask Question
12 January, 15:40

One angle of a rhombus measures 110°, and the shorter diagonal is 4 inches long. How long is the side of the rhombus? (Do not round until the final answer. Round angles to the nearest degree and side lengths to the nearest tenth of a unit.)

+4
Answers (1)
  1. 12 January, 19:18
    0
    This is the concept of geometry, we are required to calculate for the length of the sides of the rhombus; we know that a rhombus is a compressed square, this implies that all the sides are equal;

    If one of the angles is 110° the other angle will be:

    180-110=70°

    thus using the cosine rule we can find the side lengths as follows;

    c^2=a^2+b^2-2ac Cos C

    thus

    let side a=b=x in

    shorter diagonal=c=4 in

    C=70°

    substituting this into the formula we get:

    4^2=x^2+x^2-2*x*x Cos 70

    4^2=2x^2-2x^2 (0.3420)

    16=2x^2-2x^2 (0.3420)

    dividing through by 2 we get;

    8=x^2-0.3420x^2

    8=0.6580x^2

    x^2=12.15843

    getting the square root of both sides get:

    x=sqrt (12.15843

    x=3.4869)

    x=3.5 (1 d. p)

    the length of the sides is 3.5
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “One angle of a rhombus measures 110°, and the shorter diagonal is 4 inches long. How long is the side of the rhombus? (Do not round until ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers