Final answer:
To sketch the triangle and find the trigonometric functions for angle B using sides 'a = 10' and 'b = 4', we need additional information like whether the triangle is right-angled or the measurement of angle B. With that, we can use the Pythagorean theorem or the law of cosines to find the third side and then calculate the six trigonometric functions.
Step-by-step explanation:
To sketch the triangle with an angle B, we should label side 'a' as the side opposite to angle A, and side 'b' as the side adjacent to angle B since we're provided with 'a = 10' and 'b = 4'. However, the question doesn't provide us with a specific angle to use as angle B nor with the placement of the sides in relation to that angle. We can assume it wishes us to label whichever angle as B and work with given sides 'a' and 'b'. To find the values of the six trigonometric functions of angle B (sin B, cos B, tan B, csc B, sec B, and cot B) first we need to find the length of side 'c' using the Pythagorean theorem or the side opposite to angle B if it is a right-angled triangle, or by using the law of cosines if the triangle is not right-angled.
Once the length of the third side is found, we can use the basic definitions of trigonometric functions to find all six functions for angle B:
- sin B = opposite side/hypotenuse
- cos B = adjacent side/hypotenuse
- tan B = opposite side/adjacent side
- csc B = 1/sin B
- sec B = 1/cos B
- cot B = 1/tan B
Without additional information such as whether the triangle is right-angled or not, or the specific measurement of angle B, we're unable to provide the exact values for the trigonometric functions.