? asked in Education & ReferenceHomework Help · 10 years ago

I need some help on this geometry problem, its really confusing. Please and thank you?

Pete is building a kite. (You draw a kite and the top left and right corners are 2 feet and the bottom left and right corners are 3 feet.) But the length on the side is 4 ft.) Now find the measure of the given angle the 2-foot edge makes with the 3-foot edge.

And these answer selections don't match up with the problem. (F=104.5, G=85.2, H=60 J=14.5)

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  • 10 years ago
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    In spite of what you posted, the answer selections DO match up with this problem.

    Drawing the kite with those dimensions, you have a deltoid quadrilateral. Make sure you draw the 4 foot dimension is the height of the kite, from corner to top corner.

    Therefore, this forms two congruent triangles that have one short side 2 feet long, another side 3 feet long, and a large side 4 feet long. The large side is shared between the two congruent triangles.

    Look at the figure in the source link I posted below. The 2 foot sides are AB and AD. The 3 foot sides are BC and DC. The 4 foot side is AC.

    The two congruent triangles are ABCA and ACDA.

    Since we know the three sides of both triangles, we use the Law of Cosines to calculate angles.

    The Law of Cosines state C² = A² + B² - 2AB*cosθ where θ is the angle opposite side C. In the figure at the source link I posted below, this angle is angle ABC and angle ADC.

    In this problem, if you assign 2 feet to A and 3 feet to B and 4 feet to C, then θ will be the angle opposite the 4 foot side. That means that θ is the angle formed between the 2 foot and 3 foot sides, and that is what this problem is asking us to calculate.

    solving for cosθ, we have

    cosθ = -(c² - a² - b²)/2ab

    cosθ = (-c² + a² + b²)/2ab

    cosθ = (a² + b² - c²)/2ab

    Taking the inverse cosine (arccos) of both sides of the equal sign, we have:

    θ = arccos((a² + b² - c²)/2ab) where θ is in degrees

    So plugging in the values we already know;

    θ = arccos((2² + 3² - 4²)/(2*2*3))

    θ = arccos((4 + 9 - 16)/(12))

    θ = arccos(-3/12)

    θ = 104.5º (the angle between the 2 foot side and the 3 foot side)

    Now compare this answer (104.5º) with the answer selections you posted above. Can you find it now?

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