In a figure, ABCD is a rectangle in which AD=43.7 cm, DE=100 cm and EDC =27°, where E is a point above C making a rught angled triangle DEC above the rectangle.
Find angle EAD.
I found the other parts of this question but thjs one's difficult. I assumed AB as the rectangle's base and DC as the triangle's basee i.e the top of the rectangle.
Thanks
To find angle EAD, we can use the property that angles in a triangle add up to 180 degrees.
Since ABCD is a rectangle, AD is parallel to BC. Therefore, angle EAD and angle EDC are corresponding angles and they are equal.
We are given that angle EDC is 27 degrees. Therefore, angle EAD is also 27 degrees.
To find angle EAD, we can start by drawing a diagram and labeling the given information. From the problem statement, we know that ABCD is a rectangle with AD = 43.7 cm. DE = 100 cm, and ∠EDC = 27°.
To find angle EAD, we need to use the properties of a rectangle. Since ABCD is a rectangle, opposite sides are equal in length. Therefore, AB = CD = 43.7 cm.
Now let's consider triangle ADE. We have DE = 100 cm, AD = 43.7 cm, and we want to find angle EAD.
To find angle EAD, we can use the trigonometric function tangent (tan). The tangent of an angle can be found by dividing the length of the side opposite the angle (DE) by the length of the side adjacent to the angle (AD).
In this case, tan(EAD) = DE / AD = 100 cm / 43.7 cm.
Next, we can use the inverse tangent (arctan) function to find the angle EAD. Taking the inverse tangent of both sides of the equation, we have:
EAD = arctan(100 cm / 43.7 cm).
Using a calculator to evaluate the arctan(100 cm / 43.7 cm), we find that angle EAD is approximately 66.06°.
So, angle EAD is approximately 66.06°.
ADE=90+27=117°
using the law of cosines,
AE^2 = 43.7^2 + 100^2 - 2*43.7*100*cos117°
So, AE=126
Now use the law of sines:
sin(EAD)/100 = sin(117°)/126